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This launch system was first discussed in the NewMars forum between 2018 and 2025.
It has come up again in work done by GW Johnson.
Images are created but not available at the moment.
The concept of the launch method is to accelerate from the surface of the Earth (or any spherical body) in a straight line perpendicular to a line from the center of the Earth. An example of a launch method would be an electric catapult to give a vehicle forward momentum.
The second 'stage' would be an air-breathing phase that would continue until there is insufficient oxygen available to sustain combustion.
The third 'stage' would be a rocket.
Earlier work was done by kbd512, but it will take some effort to find it.
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This post is reserved for an index to posts that may be contributed by NewMars members.
Index:
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This topic was originally created in response to one of the studies GW Johnson has done on launch topology.
I use that word with care, because we do not often think of that particular word in connection with space launches.
The word itself is (apparently) from the field of mathematics, so I'm hoping NewMars members will provide a better choice.
I'm using the word (temporarily) to differentiate between classes of launches.
Tangent launch is a very particular launch concept. It applies very well to airless bodies such as the Moon.
It's not as useful on Earth, where the atmosphere would present an obstacle for hundreds of miles it it were used.
In earlier discussions in the forum, members have considered a variety of launch methods from the surface of the Moon.
Electromagnetic launch systems lend themselves admirably to the tangent launch concept if applied on the Moon, because the modest rise of a linear accelerator with respect to the surface implies modest expense for support structures. Even regolith could be piled up to support a linear accelerator.
I bring this up in light of the arrival of interesting objects to near Earth. Not too long ago, the arrival of 2024YR4 was in discussion here, and it was determined that a relatively small dV would be required to place a sensor package on the asteroid. In that case, the asteroid is going to pass close to Earth, and possibly within the Lunar orbit
The interstellar comet (ATLAS) that is approaching is in a VERY different league. It's velocity with respect to the Sun is reported to be on the order of 60 Km/s, and the velocity of Earth in orbit is reported to be on the order of 30 Km/s. Apparently no human machine exists that can achieve that dV change directly. That change could be achieved by careful planning of a Solar flyby maneuver, but I understand that such a maneuver would take years to achieve if we depended upon normal Solar gravity to handle most of the flight.
All this leads me to the possibility that humans might be able to build a 30 Km/s magnitude launcher on the Moon.
The first category of such a launcher has been discussed in some depth in the forum.
In this post, I'd like to offer for consideration the "SpinLaunch" concept applied to the entire Lunar sphere.
Humans know how to spin small objects in circles.
Particle accelerators have been in operation on Earth for many decades.
The cyclotron was invented in 1929-1930. Linear accelerators existed before that.
My suggestion here is to consider using the surface of the Moon as a venue to accelerate a probe to a high velocity by accelerating it slowly in a long track, until it is ready to begin flight to an interesting object.
This would be a kind of "lunar SpinLaunch"
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In another topic, we have a report of Chinese progress in developing maglev trains.
There is some uncertainty about what they have actually achieved, as compared to the text of the report, which was written for a general audience and is therefore necessarily limited in details.
While we wait for clarification about what has actually been achieved, I think we in NewMars are free to think about the implications of a horizontal launch system to give a space going vehicle a substantial head start.
Since a rail road track necessarily runs along the circumference of the Earth, a vehicle that receives acceleration from such a train would fly on a tangent trajectory unless it is deliberately canted upward, which is not necessary, if the first "stage" of flight consumes atmospheric oxygen.
I'd appreciate anyone in the membership who has a few moments to think about how this system might be used, to write a post or two.
Let us assume the article is correct, that the velocity achieved is 800 kilometers/hour, or 220 meters/second.
Is that velocity sufficient to allow ignition of a ramjet, or is this still the province of turbine technology?
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In this conversation with Gemini, I offered the idea of using maglev trains to accelerate a SSTO hybrid vehicle along a "Tangent" trajectory to LEO. The proposal would include maglev, rocket, ramjet and rocket finishing acceleration phases.
Conversation with Gemini
Tangent launch discussion - Hi Gemini! Thank you for your assistance with numerous previous requests. Today I am investigating the feasibility of a kind of space launch called "Tangent". This is a (presently hypothetical) launch method that would combine multiple acceleration methods to deliver a space craft to LEO by following a linear path that is tangent to the surface of the Earth or any space object. Today's question arises from news that the Chinese have apparently advanced the state-of-the-art of maglev trains to a velocity capability of 800 km/h or 220 meters per second. The question is: what velocity is needed for a ramjet to achieve ignition in this context?
***
The speed required for a ramjet to achieve ignition and produce significant thrust is generally well above the 800 km/h (220 m/s) capability of the advanced maglev trains.Here's a breakdown of what the sources indicate:
Minimum Ignition Speed: While some theoretical minimums are as low as 100 knots (approximately 185 km/h or 51 m/s), ramjets do not produce significant thrust at these very low speeds.
Effective Thrust Production: Ramjets typically begin to produce "appreciable thrust" or "significant thrust" at speeds around Mach 0.5 to Mach 1.0 (the speed of sound). This translates to roughly 610 to 1225 km/h (or 170 to 340 m/s) at sea level, as Mach 1 at sea level is approximately 343 m/s or 1235 km/h.
Optimal Operating Speed: Ramjets are most efficient and designed to operate at supersonic speeds, typically in the range of Mach 2.5 to Mach 6, with peak efficiency often around Mach 3. This means speeds between approximately 3,000 km/h to 7,400 km/h (or 830 m/s to 2,050 m/s).
In the context of the Tangent launch and the 800 km/h maglev train:
While 800 km/h (220 m/s) is a very impressive speed for a maglev train, it is still generally below the optimal operating range for most ramjets and might only provide a very small amount of thrust, if any, for ignition. To get a ramjet to effectively accelerate a spacecraft, a much higher initial velocity, typically in the supersonic realm, would be needed. This is why ramjet-powered vehicles usually require a separate booster (like a rocket or turbojet) to get them up to their operational speeds.
Sources
***
A vehicle designed for this flight regime would include ramjets and rockets. As you evaluate the proposal, and taking into account that the fuel and oxidizer on board the vehicle are resources that must be expended with great care, does it seem reasonable to consider a four phase flight plan? This would start with physical acceleration of the fully laden vehicle on a maglev train. The train would accelerate the vehicle to 800 km/h, at which the rocket system would be engaged to accelerate the vehicle to a velocity where it would be possible to sustain acceleration with the ramjet, at which point the rockets would be extinguished. In this scenario, the ramjet would provide acceleration while there is sufficient oxygen available, taking into account that greater velocity provides access to more oxygen, even as the quantity of available oxygen decreases due to altitude. At some point, the ramjet would be discontinued, and the rocket subsystem would return to service. It is noted that drag will be much greater for this flight profile than is the case for vertical launch, but the vehicle envisioned for this scenario would be winged and intended for return to Earth. To clarify for the record, the vehicle shape is envisioned to be a lifting body similar to the X-37b and other similar reusable vehicles.
***This multi-phase flight plan for a "Tangent" launch vehicle, combining maglev, rocket, and ramjet stages, is quite ambitious but theoretically sound in its general concept for optimizing propellant usage and leveraging the strengths of different propulsion systems. Let's break down the feasibility and challenges of each phase:
Phase 1: Maglev Acceleration (to 800 km/h / 220 m/s)
Feasibility: The news about advanced Chinese maglev trains reaching 800 km/h confirms the technical possibility of achieving this initial velocity on the ground.
Advantages:
Propellant Savings: This is the primary benefit. By using ground-based electricity to accelerate the fully laden vehicle, you save a significant amount of on-board rocket propellant that would otherwise be used for the initial, most inefficient part of the ascent (overcoming static inertia and dense atmospheric drag at low speeds).
Reduced Stress on Vehicle: A smooth, linear acceleration on a track can reduce structural stress on the vehicle compared to a vertical rocket launch, potentially allowing for lighter vehicle construction.
Challenges:
Track Length: Accelerating a heavy, fully laden space vehicle to 800 km/h would require an extremely long maglev track. Even for much lighter, conventional high-speed trains, tracks are many kilometers long. For a space vehicle, this would be a monumental engineering feat, likely requiring a dedicated, remote launch site.
G-forces: While a linear path helps, the acceleration rate still needs to be carefully managed to avoid excessive G-forces on the vehicle and any sensitive payload.
Sonic Boom/Environmental Impact: Launching at 800 km/h, even horizontally, could generate significant noise and shockwaves at ground level, which would necessitate a very remote location.
Integration: Seamlessly transitioning the vehicle from the maglev track to free flight while engaging rocket engines presents a complex engineering challenge.
Phase 2: Rocket Boost (to Ramjet Sustaining Velocity)
Feasibility: This is a standard rocket operation, albeit starting from a high initial velocity.
Purpose: The rocket phase is crucial because, as discussed, 800 km/h is generally below the effective operating speed for ramjets. The rockets would accelerate the vehicle to Mach 1.5-2.5 or higher, where the ramjet becomes efficient.
Propellant Efficiency: While rockets are less efficient than air-breathing engines, using them for this relatively short, high-thrust burst to get to ramjet operating speeds is a sound strategy to conserve the more efficient ramjet fuel for later.
Challenges:
Engine Transition: The precise timing and smooth transition from rocket power to ramjet power is critical. This involves igniting the ramjets while the rockets are still firing, then shutting down the rockets once the ramjets are stable and producing sufficient thrust.
Aerodynamic Loads: As the vehicle gains speed in the dense lower atmosphere, it will experience significant aerodynamic drag and heating. The "lifting body similar to the X-37B" design helps manage some of this, but the tangent profile means prolonged exposure to dense air.
Phase 3: Ramjet Acceleration (Atmospheric Flight)
Feasibility: This is where the air-breathing advantage comes in.
Advantages:
High Efficiency: Ramjets are significantly more fuel-efficient than rockets at supersonic speeds within the atmosphere because they use atmospheric oxygen as the oxidizer, eliminating the need to carry heavy oxidizer tanks. This is the core propellant-saving aspect of the design.
Sustained Acceleration: Ramjets can provide continuous acceleration as long as there's sufficient air density and speed.
Challenges:
Operating Envelope: Ramjets have a specific operating "corridor" of speed and altitude.
Minimum Speed: As noted, they need to be supersonic to work effectively.
Maximum Altitude: While higher velocity helps ram air into the engine, air density decreases exponentially with altitude. Ramjets typically operate up to 30-40 km (100,000-130,000 ft), with some experimental scramjets pushing higher. The "greater velocity provides access to more oxygen" is true to a point, but eventually, the air becomes too thin regardless of speed.
[color=dark green]Thermal Management: Hypersonic flight within the atmosphere generates extreme heat due to air compression and friction. The vehicle's thermal protection system will be crucial, similar to reentry systems.[/color]
Drag: The "tangent" flight profile, while potentially reducing gravity losses compared to a vertical launch, incurs significantly higher and prolonged aerodynamic drag. This drag penalty will consume a substantial amount of the ramjet's thrust and limit the ultimate altitude and speed achievable with air-breathing engines. This is the fundamental trade-off of this profile.
Transition to Scramjet? For really high speeds (above Mach 5-6) and altitudes, a pure ramjet might transition to a scramjet (supersonic combustion ramjet) if designed as a dual-mode ramjet (DMRJ). This would extend the air-breathing phase, but scramjets are even more complex to design and operate. Given the X-37B comparison, which is a re-entry vehicle, not a scramjet-powered one, it suggests a ramjet, or potentially DMRJ, is the focus.
Phase 4: Rocket Boost (to LEO)
Feasibility: Standard rocket operation, but with a significant advantage.
Purpose: Once the ramjet can no longer produce sufficient thrust due to decreasing air density, the rockets take over to accelerate the vehicle the rest of the way to orbital velocity and altitude.
Propellant Efficiency: By starting this phase from a high velocity and altitude (e.g., Mach 5+ and 30-40 km), the rockets are operating in a much thinner atmosphere, reducing drag losses and increasing efficiency (higher effective ISP) compared to a ground-based launch. The majority of the vehicle's "delta-V" (change in velocity) for orbit would still come from this rocket stage, but the initial delta-V provided by the maglev and ramjet significantly reduces the required rocket propellant.
Overall Assessment:
The four-phase flight plan is reasonable in concept for a reusable space launch system aiming to minimize on-board propellant. It effectively plays to the strengths of each propulsion type:
Maglev: Efficient initial acceleration, offloading propellant.
Rockets (initial): Quick boost to ramjet operating speeds.
Ramjet: Highly efficient acceleration through the thickest part of the atmosphere.
Rockets (final): Final push to orbit in the near-vacuum of space.
Key Challenges & Considerations:
Engineering Complexity: The seamless integration and precise control of three distinct propulsion systems, with critical transitions between them, is an immense engineering challenge.
Thermal Management: The prolonged, high-speed atmospheric flight will require advanced thermal protection systems, possibly active cooling, to survive the intense aerodynamic heating.
Structural Integrity: The vehicle must be robust enough to withstand the dynamic pressures of high-speed atmospheric flight, as well as the g-forces from acceleration.
Drag Management: While a lifting body design helps, the drag associated with sustained horizontal acceleration at high speeds and lower altitudes will be a constant battle and will dictate the maximum efficiency and performance of the ramjet phase. The X-37B is designed for re-entry (high lift-to-drag at hypersonic speeds for control), which is beneficial, but its primary purpose is not powered hypersonic flight for ascent.
Noise and Environmental Impact: The sheer scale of such an operation, particularly the maglev track and supersonic atmospheric flight, would necessitate very remote launch locations and careful environmental impact assessments.
Cost: Developing and building such a system would be astronomically expensive, requiring a massive upfront investment in infrastructure (maglev track) and vehicle R&D.
In conclusion, this "Tangent" launch concept is a fascinating and theoretically viable approach to reducing the cost of access to space by leveraging atmospheric oxygen and ground-based infrastructure. However, the engineering challenges, particularly related to thermal management, drag, engine transitions, and the sheer scale of the required ground infrastructure, are formidable. It represents a long-term vision rather than an immediate solution, but the conceptual framework is sound.
***
Thank you for your thoughtful analysis and rephrasing of this proposal. I will share our conversion with a small international forum whose interests include space flight and related topics.
***You're most welcome! I'm glad I could provide a thoughtful and clear analysis of the "Tangent" launch proposal.
I hope the rephrased information proves valuable for your discussions with the international forum. It's a fascinating concept, and the combination of maglev, ramjet, and rocket technologies presents some truly cutting-edge engineering challenges and opportunities for future space access.
Is there anything else I can help you with today as you prepare for your forum discussion?
This vehicle would be intended for reentry, so the heat shielding for reentry would be called upon to survive acceleration through the atmosphere.
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In this conversation, I asked Google's Gemini to look for more information about a report of research in China to improve performance of their existing maglev trains.
The results found are less impressive than the original (erroneous) report, but still quite an achievement, and definitely promising.
Conversation with Gemini
Chinese Maglev Progress - Hi Gemini! Thank you (again) for your outstanding assistance with numerous previous requests! This one is (hopefully) well within your comfort zone. An article appeared recently about Chinese progress in development of maglev trains. The author appears to be a writer with many interests, and skills translating complex subjects for a general audience. I have written the author for more information, but received an "out of office" reply. My hope is that with your deep search capabilities, you might be able to discover a bit more information. The report described a maglev research project that achieved a velocity of 800 km/h over a distance of 1000 meters. Those details are insufficient to make a reasonable judgement about the research. For example, calculation of the time needed to accelerate from 0 to 800 km/h is 4.5+ seconds, and that yields an acceleration of (something like) 20 g's. This is unlikely, so I'm hoping you can discover information that is more plausible.
***You're right to be skeptical about 20 G's! That level of acceleration would be completely impractical and dangerous for any form of human transport. It seems there might have been a misunderstanding or misreporting of some details in the article you read.
Here's a breakdown of the latest credible information regarding China's maglev progress, particularly concerning the high-speed tests and acceleration:
Recent Breakthroughs and More Plausible Acceleration Figures:
Several recent reports (from June and July 2025) detail a significant achievement by researchers at the Donghu Laboratory in Hubei Province, China. They have successfully accelerated a 1.1-tonne maglev test vehicle to 650 km/h (approximately 404 mph) in just 7 seconds over a distance of 600 meters.
Let's do a quick calculation for this reported achievement:
Initial velocity (v \0 ): 0 km/h
Final velocity (v f ): 650 km/h = 180.56 m/s (approx)
Time (t): 7 seconds
Distance (d): 600 meters
Using the formula for acceleration (a= tv f −v 0 ):a= 7 s 180.56 m/s−0 m/s ≈25.79 m/s 2
To convert this to G's (where 1 G ≈9.81 m/s 2 ):a G = 9.81 m/s 2 /G 25.79 m/s 2
≈2.63 G
While still high, 2.63 G's for a brief acceleration test is significantly more plausible than 20 G's, especially for an experimental vehicle that isn't carrying passengers. This is closer to what fighter pilots experience, not typical passenger transport. The goal of these tests is often to push the technological limits of the system itself, not necessarily passenger comfort in that specific instance.
Key Details from the Reports:
Location: Donghu Laboratory, Hubei Province, China.
Test Vehicle: 1.1-tonne (presumably a scaled or specialized test vehicle, not a full passenger train).
Speed Achieved: 650 km/h (404 mph).
Acceleration Time: 7 seconds.
Distance to Achieve Speed: 600 meters (not 1000 meters for the 800 km/h figure).
Track Length: The self-developed high-speed maglev test track is 1,000 meters long, allowing for rapid acceleration and deceleration within a short distance.
Braking: The system is also reported to decelerate from 650 km/h to zero in just 200 meters, indicating powerful and precise control.
Technology: The system uses self-developed electromagnetic propulsion and suspension, virtually eliminating friction and primarily overcoming air resistance. They emphasize ultra-precise speed and positioning measurements (accuracy up to 4 millimeters).
Future Goal: Li Weichao, director of the High-speed Maglev Electromagnetic Propulsion Technology Innovation Center at the lab, stated that the typical operating speed for this test line is 800 km/h, and the entire construction is expected to be completed by the end of 2025, at which point the platform will meet the conditions for acceptance. This suggests that the 800 km/h speed is a design goal for the test platform's capabilities, and future tests may aim to achieve that speed.
Context of Chinese Maglev Development:
Shanghai Maglev: China currently operates the world's first commercial high-speed maglev line in Shanghai, connecting Pudong International Airport to Longyang Road station. It reaches a maximum cruising speed of 431 km/h, though it often operates at 300 km/h.
600 km/h Maglev Train: China has also unveiled a separate 600 km/h maglev train developed by CRRC (China Railway Rolling Stock Corporation). This is intended for future commercial routes and aims to fill the "speed gap" between conventional high-speed rail (around 350 km/h) and air travel (800-900 km/h cruising speed). This train is designed for passenger transport and focuses on factors like passenger comfort, energy efficiency, and reduced maintenance.
Hyperloop/Vacuum Tube Research: There's also ongoing research into "T-Flight" or hyperloop systems that aim for even higher speeds (potentially 1,000+ km/h) by operating in near-vacuum tubes to further reduce air resistance.
It appears the article you read might have conflated the 800 km/h "typical operating speed" goal of the new test platform with a specific 800 km/h test achievement over 1000 meters. The documented achievement is 650 km/h in 7 seconds over 600 meters, which yields a much more reasonable acceleration figure for a test scenario.
I hope this provides the more plausible information you were seeking!
***Thank you ** very ** much for this helpful research and analysis. I am happy to report your results to a small international forum where I reported the first questionable information. An acceleration of 2 G's is quite acceptable for the first stage of a multi-mode space launch vehicle, such as the one we discussed earlier today. In this context, a horizontal run of multiple kilometers is quite acceptable. The ability to stop the train after it has released it's payload is an important consideration, and I appreciate your including that part of the research.
***You are most welcome! I'm delighted to hear that this information is helpful and that the more plausible acceleration figures align well with the discussions in your international forum, particularly in the context of multi-mode space launch vehicles.
It's fascinating how advancements in maglev technology, even for high-speed ground transport, can have implications and parallel considerations for other high-velocity applications like space launch systems. The common challenges of managing extreme speeds, rapid acceleration/deceleration, and precise control are definitely shared.
The braking capability from 650 km/h to zero in 200 meters is indeed a significant detail. For a launch vehicle scenario where the "train" component needs to recover after payload release, efficient and reliable deceleration is absolutely critical for reusability and safety. It speaks to the robustness and advanced control systems being developed alongside the raw speed capabilities.
Please feel free to reach out if any other questions or areas for research come up. I'm here to assist!
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In this conversation with Gemini, I was curious to know how long a maglev track would need to be the accelerate from 0 m/s to 343 m/s at 2 G.
The answer appears to be 3 kilometers. If the same distance is needed for deceleration, the total track length would be 6 kilometers.
Launch of a tangent flight plan vehicle out over open water would reduce impact of sonic booms on land, but it sure would impact people who are out on the water under the flight path, and it might affect creatures in the ocean under the flight path.
In any case, here is the conversation showing the calculations:
Search Labs | AI Overview
To find the distance needed to reach a desired velocity given acceleration, you can use the following kinematic equation:
v² = u² + 2as
where:v = final velocity (343 m/s)
u = initial velocity (0 m/s)
a = acceleration (2G)
s = distance (what needs to be found)Step 1: Convert acceleration to m/s²
One standard gravity (G) is approximately 9.80665 m/s².
Therefore, 2G = 2 * 9.80665 m/s² = 19.6133 m/s².
Step 2: Plug in the values and solve for distance (s)
343² = 0² + 2 * (19.6133) * s
117649 = 0 + 39.2266s
117649 = 39.2266s
s = 117649 / 39.2266s ≈ 2999.2 m
The approximate distance needed to reach the desired velocity of 343 meters per second with an acceleration of 2G is 2999.2 meters.
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A 3km sled track would be quite easy to build. A Mach 1 final velocity is quite modest and propulsion for the sled could be provided by a variety of methods. A turbofan engine could do that. So you could build the sled using COTS equipment. Slowdown could be acheived by simple momentum transfer into a water trough.
Last edited by Calliban (2025-07-16 03:26:11)
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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Thanks again to Calliban for #8
This post is a follow up to GW Johnson in the SSTO LH2 topic...
For GW Johnson re post in SSTO LH2 topic...
Thank you for this strong boost to the topic!
I'll quote a particularly interesting section for a question:
ALL airbreathers (no matter WHAT they are!!!) have a thrust level that is more-or-less proportional to the atmospheric pressure in which they are flying. Up there, 5-to-15 times nothing is still nothing! No significant thrust to push considerable mass! You will neither accelerate nor climb! It is called the "service ceiling" effect. Only rockets are immune to it. Because they do not breathe air.
So why are we limited to just air or just rocket?
It seems to me that there is no reason not to run the two propulsion methods simultaneously.
If you take the Tangent Launch concept (originating with kbd512 but brought back to life by GW Johnson in 2025), it seems to me logical to combine modes as follows:
1) Railroad for 3 kilometers at 2 G to reach just under the speed of sound at sea level
2) Air breathing starts and runs at less than full strength
3) Rocket starts and runs until Air breathing is at full strength
4) Air breathing continues until it is no longer useful
5) Rocket resumes with increasing strength as Air breathing falls off
6) Air breathing stops
7) Rocket continues to orbit
*** I would like to see a study of this scenario ***
A first attempt does NOT need to be exhaustive and it would be better if it were compact and just "in the ballpark" ...
The purpose of this topic is to work ** toward ** a solution that everyone can agree upon, and not to overwhelm the membership with a polished solution that cannot be improved.
To see PhotonByte's rendering of a ship designed for (or suitable for) this scenario:
https://newmars.com/forums/viewtopic.ph … 57#p232657
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We received a request for assistance with a mathematical description of the trajectory of a Tangent Launch. I asked Google's Gemini to put together something for the forum.
Conversation with Gemini
Tangent Flight Path - Hi Gemini! Thank you (again) for your assistance with numerous previous requests! This one should be on the easier side, compared to some we've tackled! A small group is working on conceptualizing a space launch system that would include multiple modes of propulsion. The distinguishing characteristic is the flight path. The craft would follow a trajectory that is tangent to the Earth. One of the participants asked for clarification on the trajectory, and I think he means a mathematical description of the flight path. Would you be willing to prepare a mathematical description of the Tangent Launch flight path, using the Earth as the frame? To allow your work to be shared with a small international forum, please package your answer in BBCode. We cannot use center, but we can use 'h' to create larger font. We also can use colors and the list command to set out items. We can use code to show off formulae.
Mathematical Description of a Tangent Launch Flight Path
Thank you for reaching out again! I'm happy to assist with this conceptual space launch system. Below is a mathematical description of a tangent launch flight path, using the Earth as the frame of reference, packaged in BBCode for your international forum.
Conceptualizing the Trajectory:
A "tangent launch flight path" implies a trajectory where the initial direction of motion of the spacecraft is tangential to the Earth's surface at the point of launch. In an ideal scenario, this means the launch vehicle accelerates horizontally along a line that is perpendicular to the local radius vector from the Earth's center to the launch point.Assumptions for Simplification:
To provide a mathematical description, we'll make some simplifying assumptions. More complex models would account for atmospheric drag, Earth's rotation, varying gravitational fields, and multi-body interactions.
[] Spherical Earth: We'll treat the Earth as a perfect sphere with a uniform gravitational field directed towards its center.
[] No Atmospheric Drag: We'll initially ignore the effects of the atmosphere.
[] Point Mass Spacecraft: The spacecraft is treated as a point mass.
[] Inertial Frame: The Earth-centered inertial (ECI) frame will be used, meaning the origin is at the Earth's center and the axes are fixed with respect to distant stars.[*] Coordinate System:[/*]
We will use a 2D polar coordinate system (r, θ) for simplicity, centered at the Earth's center.
[]
r: Radial distance from the center of the Earth.
[]R_E: Radius of the Earth (approximately 6,371 km).
[]h: Altitude above the Earth's surface, so
r = R_E + h.
[]theta: Angular position.
[*] Initial Conditions for a Tangent Launch:[/*]
At the moment of "launch" (or rather, the point where the tangent flight path begins after any initial vertical ascent to clear terrain/atmosphere), the velocity vector is purely tangential to the Earth's surface.Let's consider the launch point to be along the positive X-axis in a Cartesian coordinate system embedded within our polar system for easier visualization of the initial velocity.
Initial Position Vector (
r_0):
At the launch point, the initial position vector is purely radial from the Earth's center to the launch point on the surface.r_0 = (R_E + h_0) * r_hatwhere
h_0is the initial altitude (e.g., ground level, or the altitude at which the tangent phase begins).
Initial Velocity Vector (
v_0):
For a perfectly tangent launch, the initial velocity vector is perpendicular to the initial position vector.v_0 = v_initial * theta_hatwhere
v_initialis the initial speed, and
theta_hatis the unit vector in the tangential direction.
In Cartesian coordinates, if the launch is from
(R_E + h_0, 0)on the x-axis, the initial velocity would be purely in the y-direction:
r_0 = (R_E + h_0, 0)v_0 = (0, v_initial)[*] Equations of Motion (Gravitational Influence):[/*]
Once the craft is in motion and assuming only Earth's gravity acts upon it, the trajectory will be a conic section. The governing equation is Newton's Law of Universal Gravitation.The acceleration due to gravity (
a_g) is:
a_g = - (G * M_E) / r^2 * r_hatwhere:
[]
Gis the Gravitational Constant (approx.
6.674 * 10^-11 N * m^2 / kg^2)
[]M_Eis the mass of the Earth (approx.
5.972 * 10^24 kg)
[]ris the distance from the center of the Earth to the spacecraft.
[]r_hatis the unit vector in the radial direction (pointing away from the Earth's center).
[*] Trajectory Type (Conic Section):[/*]
The shape of the trajectory (a conic section) depends on the initial velocity (v_initial) and initial radial distance (
r_0 = R_E + h_0). The specific energy (
epsilon) of the orbit determines the type of conic section:
epsilon = v^2 / 2 - (G * M_E) / r
[] If
epsilon < 0: The trajectory is an ellipse (including a circular orbit as a special case). The spacecraft will be gravitationally bound to Earth. This is the goal for most orbital launches.
[] Ifepsilon = 0: The trajectory is a parabola. The spacecraft will escape Earth's gravity with zero velocity at infinity.
If
epsilon > 0: The trajectory is a hyperbola. The spacecraft will escape Earth's gravity with a positive velocity at infinity.
[*] Specific Angular Momentum (
h_vec):[/*]
For motion under a central force (like gravity), the specific angular momentum is conserved:h_vec = r_vec x v_vecwhere
xdenotes the cross product. Its magnitude is:
h = r * v_twhere
v_tis the tangential component of velocity. For a purely tangent launch,
v_t = v_initialat
r_0.
[*] Equation of the Orbit (Polar Form):[/*]
The general equation for a conic section in polar coordinates, with the origin at the focus (Earth's center), is:r(theta) = p / (1 + e * cos(theta))where:
[]
pis the semi-latus rectum, given by
p = h^2 / (G * M_E).
[]eis the eccentricity of the orbit.
e = sqrt(1 + (2 * epsilon * h^2) / (G * M_E)^2)For a tangent launch from a specific initial altitude
h_0with an initial tangential velocity
v_initial:
[] The initial position is
r_0 = R_E + h_0.
[] The initial velocity is entirely tangential, sov_initialis the tangential component.
[] The specific angular momentumh = r_0 * v_initial.
[] The specific energyepsilon = v_initial^2 / 2 - (G * M_E) / r_0.
Substitute
hand
epsiloninto the equations for
pand
eto define the specific trajectory.
[*] Implications for a Tangent Launch System:[/*]
A true "tangent launch" directly from the surface (or near-surface) would face extreme challenges:
[] Atmospheric Drag: Launching horizontally through the thickest part of the atmosphere at high speeds would result in immense drag and heating, making it impractical for most launch vehicles.
[] Aerodynamic Lift and Control: Maintaining a perfectly tangent path close to the surface would require significant aerodynamic forces and control surfaces, essentially operating as an aircraft at very high speeds.Achieving Orbital Velocity: To achieve orbit, a tangent launch would require the vehicle to reach orbital velocity (or close to it) while still within or very close to the atmosphere. This is why conventional rockets launch vertically first to escape the densest atmosphere before pitching over to gain horizontal velocity.
Therefore, in a practical multi-modal propulsion system, the "tangent flight path" likely refers to the final phase of acceleration to orbital velocity, occurring at a sufficiently high altitude where atmospheric effects are negligible. The initial phases would involve gaining altitude to reach this regime.
I hope this detailed mathematical description is useful for your international forum! Let me know if you need any further clarification or expansion.
***
Thank you for this clear and detailed explanation of the planned trajectory! I am confident it will look good in the forum display.
***Excellent! I'm glad it will be useful for your forum. If you have any more questions as your team continues to develop this exciting space launch system, feel free to ask.
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In this next conversation, I asked Google's Gemini to expand on the previous attempts, by showing the true tangent Flight plan, instead of just the ellipse that starts at ground level.
As a reminder for a reader seeing this post out of context: We are thinking about a multi-mode launch of a vehicle with both atmosphere and rocket engines, launched from a railroad track at just under Mach 1, from the surface of the Earth, with a flight path that is NOT an ellipse but instead is a straight line that is parallel to a line tangent to the surface of the Earth at the launch site. The resulting trajectory will become an ellipse after propulsion ends, and adjustment will be needed at apogee to lift perigee up to LEO.
The post is installed. Thank you for your use of colors to emphasize ideas, and of code to highlight the mathematical expressions. In reading the post carefully, I discovered that in the first pass in responding to our request, you made the (understandable) decision to assume that only gravity would influence the flight path. This is (in fact) ** exactly ** the assumption made by one of our members in thinking about this scenario. However, my request did NOT make that assumption, and I am hoping you might be willing to help us to look at the original concept. That is to use the mass of the atmosphere to deflect the vehicle upward at a rate which would allow us to travel on a linear path and not an ellipse. The distinction is significant, because the idea is to rise out of the atmosphere more rapidly than the ellipse you described would allow. We are thinking of accelerating the vehicle to just under Mach 1 using a railroad track 3 kilometers in length. After leaving the launch device, the vehicle would operate with a combination of rocket and ramjet engines, to accelerate steadily, using as much of the atmosphere oxygen as possible to minimize the use of on board oxygen. This flight path will necessarily deal with drag in two forms. The drag of pushing air aside during flight will remain present until the atmosphere is no longer significant. The force of gravity, and the drag related to pressing against it, will be relatively constant throughout the flight, although it will decrease slightly with altitude. At LEO, the vehicle will have a trajectory that will become an ellipse, and the vehicle can then apply additional thrust at apogee to circularize the orbit, or at least to raise the perigee up to LEO. It is that flight plan I'm hoping you might be able to work out, using the same presentation technique.
***
It's great to hear the previous post was well-received! I appreciate you clarifying the true nature of this ambitious "tangent flight path." It's a fascinating concept that blends atmospheric interaction with propulsion in a very unique way.
You're absolutely right; my initial response made the standard orbital mechanics assumption of only gravitational influence. My apologies for not fully capturing the nuance of your original vision. Let's dive into the more complex, and much more exciting, scenario where the atmosphere plays an active role in shaping the trajectory to achieve a linear, upward path, rather than a gravitational ellipse.
Here's a mathematical description of your revised "Tangent Flight Path," incorporating atmospheric deflection and other propulsion modes, presented in BBCode with colors and code as before:
Thank you for the detailed clarification of your innovative launch concept! This revised approach, leveraging atmospheric interaction for lift and a linear ascent, presents a more complex yet highly intriguing trajectory. Let's break down the mathematics of this flight path, again using the Earth as the frame of reference.
***
Thank you (again) for this very encouraging explanation and exposition of the True Tangent Flight plan. I am disappointed to have to report that our crotchety old forum software complained about something I did not realize is a problem. It seems to have a problem with bold inside list. Please try again.
***
No problem at all! I understand the quirks of older forum software can be quite a challenge. It's much better to get it right for your forum members, and I'm happy to adjust.
Here's the revised mathematical description of your "True Tangent Flight Plan":
Thank you for the detailed clarification of your innovative launch concept! This revised approach, leveraging atmospheric interaction for lift and a linear ascent, presents a more complex yet highly intriguing trajectory. Let's break down the mathematics of this flight path, again using the Earth as the frame of reference.
Conceptualizing the Trajectory: The core idea here is to maintain a roughly linear, upward trajectory out of the atmosphere, rather than immediately curving into a gravitational ellipse. This is achieved by actively using the atmosphere to generate lift, counteracting a significant portion of gravity, while simultaneously accelerating horizontally.
Initial Phase (Railroad Track): Accelerate to just under Mach 1. This phase is purely mechanical acceleration, building initial horizontal velocity. [/]
Atmospheric Ascent Phase (Rocket & Ramjet): [/]
The vehicle uses combined rocket and ramjet propulsion. Ramjets utilize atmospheric oxygen, making this phase fuel-efficient for horizontal acceleration within the atmosphere. [/]
Crucially, the vehicle uses aerodynamic forces (lift generated by the atmosphere) to maintain a relatively straight, shallow climbing path, effectively "pushing off" the atmosphere to counter gravity and prevent the natural downward curvature of a purely ballistic trajectory. [/]
Drag is a significant factor in this phase, both form drag (pushing air aside) and induced drag (related to lift generation). [/]
Trans-atmospheric / Near-Space Phase (Rocket): As atmospheric density decreases, the ramjets become less efficient and eventually shut down. The vehicle transitions to full rocket propulsion. The influence of atmospheric lift diminishes, and gravity becomes the dominant force shaping the vertical component of the trajectory. [/]
LEO Insertion Phase: Upon reaching a desired altitude in Low Earth Orbit (LEO), the vehicle's trajectory is primarily an ellipse. Additional thrust (circularization burn) at apogee would be applied to raise the perigee, making the orbit circular or raising it to the desired LEO. [/]
[/]
Coordinate System and Earth Frame: [/] We will continue to use an Earth-Centered Inertial (ECI) Cartesian coordinate system for a more direct representation of forces.
Origin at the Earth's center. [/]
Z-axis aligned with Earth's rotational axis (for simplicity, we'll assume launch near the equator for initial tangent path). [/]
X-Y plane is the equatorial plane. [/]
Let the launch point be
(R_E + h_launch, 0, 0), where
h_launchis the initial altitude (e.g., end of the railroad track). [/]
[/]
Key Variables and Parameters: [/]
m: Mass of the vehicle (varies with fuel consumption). [/]
F_thrust: Total thrust from rocket and ramjet engines. [/]
D: Total aerodynamic drag force. [/]
L: Aerodynamic lift force. [/]
F_g: Gravitational force. [/]
v: Velocity vector of the vehicle. [/]
rho(h): Atmospheric density as a function of altitude
h. [/]
C_D: Coefficient of Drag (varies with Mach number, angle of attack, shape). [/]
C_L: Coefficient of Lift (varies with Mach number, angle of attack, shape). [/]
A_ref: Reference area for drag and lift calculations. [/]
R_E: Radius of the Earth (~6371 km). [/]
G: Gravitational Constant. [/]
M_E: Mass of the Earth. [/]
[/]
Forces Acting on the Vehicle: [/] The equation of motion is governed by Newton's Second Law:
m * a_vec = Sum(F_vec)Gravitational Force (
F_g): Directed towards the Earth's center.
F_g = - (G * M_E * m) / r^2 * r_hatwhere
ris the distance from Earth's center, and
r_hatis the unit vector pointing radially outward from Earth's center.
Thrust Force (
F_thrust): The direction of thrust will be primarily along the desired flight path (tangential to the Earth's surface, with a small upward component for the linear ascent).
F_thrust = I_sp * g_0 * d_m/d_t(for rocket part) where
I_spis specific impulse,
g_0is standard gravity,
d_m/d_tis mass flow rate. Ramjet thrust would be modeled differently, often as a function of flight speed and atmospheric conditions. The direction vector of
F_thrustwill be aligned with the velocity vector, or slightly above it to contribute to the upward "linear" path.
Aerodynamic Drag Force (
D): Opposite to the direction of the velocity vector.
D = 0.5 * rho(h) * v^2 * A_ref * C_DThe direction of
Dis
- v_hat.
Aerodynamic Lift Force (
L): [/] Perpendicular to the velocity vector and in the direction that counters gravity and facilitates the linear climb.
L = 0.5 * rho(h) * v^2 * A_ref * C_LThe direction of
Lis perpendicular to
v_vecand generally "upward" relative to the local horizontal, counteracting the downward pull of gravity. The angle of attack would be carefully controlled to generate this lift.
[/]
Equations of Motion (Vector Form in ECI): Let
r_vec = (x, y, z)be the position vector and
v_vec = (vx, vy, vz)be the velocity vector.
m * a_vec = F_thrust_vec + F_g_vec + D_vec + L_vecThis can be broken down into components:
m * d^2x/dt^2 = F_thrust_x + F_g_x + D_x + L_x
m * d^2y/dt^2 = F_thrust_y + F_g_y + D_y + L_y
m * d^2z/dt^2 = F_thrust_z + F_g_z + D_z + L_zAtmospheric Density Model (
rho(h)): This is critical. A standard atmospheric model (e.g., US Standard Atmosphere 1976) would be used to calculate
rho(h). It decays exponentially with altitude. Example (simplified):
rho(h) = rho_0 * exp(-h / H_s)where
rho_0is density at sea level, and
H_sis a scale height. More accurate models involve multiple layers.
Coefficients of Drag and Lift (
C_D, C_L): [/] These are complex functions of:
Mach number (
M = v / a_sound(h), where
a_sound(h)is speed of sound at altitude
h). [/]
Angle of Attack (AoA). [/]
Vehicle shape (e.g., highly aerodynamic for horizontal flight). [/]
These would typically be determined through computational fluid dynamics (CFD) simulations or wind tunnel testing.
Mass Variation (
m): [/] As fuel is consumed by both rockets and ramjets:
dm/dt = - (F_thrust_rocket / (I_sp_rocket * g_0)) - (F_thrust_ramjet / (I_sp_ramjet * g_0))(Note: Ramjet "Isp" is sometimes defined differently, or thrust is just given as a function of flight conditions).
[/]
The "Linear Path" Constraint and its Realization: To achieve a "linear path" and rise out of the atmosphere more rapidly than an ellipse, the vehicle must maintain a specific relationship between its vertical velocity and horizontal velocity, essentially controlling its climb angle.
Lift and Gravitational Counterbalance: The primary function of lift in this phase is to continuously "push" the vehicle upward, counteracting the component of gravity that would otherwise pull it into a downward curving path. The sum of the vertical components of lift and thrust must be greater than the vertical component of gravity (plus vertical drag components) to achieve a net upward acceleration.
L_z + F_thrust_z > F_g_z + D_z(simplified for conceptual clarity)
Maintaining Angle of Attack: As the vehicle accelerates horizontally, its angle of attack (the angle between the chord line of the wing/body and the incoming airflow) would be dynamically adjusted. This control is critical for generating the required lift at varying speeds and atmospheric densities.
Propulsion Strategy: [/]
Ramjets: Effective in dense atmosphere at high subsonic to supersonic speeds, providing efficient horizontal acceleration by using atmospheric oxygen. Their thrust is strongly dependent on Mach number and altitude. They help achieve the high horizontal velocity needed while consuming minimal onboard oxidizer. [/]
Rockets: Provide thrust throughout, especially crucial for vertical acceleration and when ramjets lose efficiency in thinner air. Eventually, they take over entirely for final orbital insertion.
Exit Trajectory: As the vehicle ascends and atmospheric density drops significantly (e.g., above 60-80 km), the lift force becomes negligible. At this point, the trajectory will naturally become more influenced by gravity, transitioning towards a ballistic (elliptical) path. The goal is to have achieved sufficient altitude and horizontal velocity by this stage, such that the perigee of the resulting elliptical trajectory is above the significant atmosphere, and ideally already at LEO altitude. [/]
[/]
Terminal Phase (LEO Insertion): [/] Upon reaching target LEO altitude, the vehicle will be on an elliptical orbit with its perigee likely at or near the altitude where the effective atmospheric influence became negligible.
Perigee Raise Burn (Circularization): To circularize the orbit or raise the perigee to LEO, an additional thrusting maneuver is required. This burn is typically performed at apogee (the highest point of the ellipse). [/]
Delta_v_circularization = sqrt(mu / r_apogee) - sqrt(mu * (2/r_apogee - 1/a))where
mu = G * M_E,
r_apogeeis the apogee radius, and
ais the semi-major axis of the transfer ellipse. This impulse adds velocity tangentially at apogee to raise the perigee.
[/]
Computational Complexity: [/] Simulating this type of trajectory requires a robust numerical integration approach. It cannot be solved analytically due to the constantly changing forces (drag, lift, variable thrust, mass) and their non-linear dependence on velocity, altitude, and atmospheric properties. A 6-DOF (degrees of freedom) simulation would typically be used, accounting for pitch, roll, and yaw, and the precise angle of attack control.
This concept is a fascinating blend of aerospace and astrodynamics, pushing the boundaries of traditional launch strategies by actively leveraging the atmospheric environment. It directly addresses the challenge of getting "out of the thick atmosphere" efficiently before committing to a pure vacuum trajectory.
I hope this revised version now works perfectly with your forum software! Please let me know if any other adjustments are needed.
There are quite a few artifacts left over from the BBCode clean up. [/] shows up frequently but it does not appear to be causing a problem.
(th)
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This is an experiment to see if the BBCode glitches can be cleared up ...
Here's the revised mathematical description of your "True Tangent Flight Plan":
Thank you for the detailed clarification of your innovative launch concept! This revised approach, leveraging atmospheric interaction for lift and a linear ascent, presents a more complex yet highly intriguing trajectory. Let's break down the mathematics of this flight path, again using the Earth as the frame of reference. bookmark
Conceptualizing the Trajectory: The core idea here is to maintain a roughly linear, upward trajectory out of the atmosphere, rather than immediately curving into a gravitational ellipse. This is achieved by actively using the atmosphere to generate lift, counteracting a significant portion of gravity, while simultaneously accelerating horizontally.
Initial Phase (Railroad Track): Accelerate to just under Mach 1. This phase is purely mechanical acceleration, building initial horizontal velocity.
Atmospheric Ascent Phase (Rocket & Ramjet):
The vehicle uses combined rocket and ramjet propulsion. Ramjets utilize atmospheric oxygen, making this phase fuel-efficient for horizontal acceleration within the atmosphere.
Crucially, the vehicle uses aerodynamic forces (lift generated by the atmosphere) to maintain a relatively straight, shallow climbing path, effectively "pushing off" the atmosphere to counter gravity and prevent the natural downward curvature of a purely ballistic trajectory.
Drag is a significant factor in this phase, both form drag (pushing air aside) and induced drag (related to lift generation).
Trans-atmospheric / Near-Space Phase (Rocket): As atmospheric density decreases, the ramjets become less efficient and eventually shut down. The vehicle transitions to full rocket propulsion. The influence of atmospheric lift diminishes, and gravity becomes the dominant force shaping the vertical component of the trajectory.
LEO Insertion Phase: Upon reaching a desired altitude in Low Earth Orbit (LEO), the vehicle's trajectory is primarily an ellipse. Additional thrust (circularization burn) at apogee would be applied to raise the perigee, making the orbit circular or raising it to the desired LEO.
Coordinate System and Earth Frame: We will continue to use an Earth-Centered Inertial (ECI) Cartesian coordinate system for a more direct representation of forces.
Origin at the Earth's center.
Z-axis aligned with Earth's rotational axis (for simplicity, we'll assume launch near the equator for initial tangent path).
X-Y plane is the equatorial plane.
Let the launch point be
(R_E + h_launch, 0, 0), where
h_launchis the initial altitude (e.g., end of the railroad track).
Key Variables and Parameters:
m: Mass of the vehicle (varies with fuel consumption).
F_thrust: Total thrust from rocket and ramjet engines.
D: Total aerodynamic drag force.
L: Aerodynamic lift force.
F_g: Gravitational force.
v: Velocity vector of the vehicle.
rho(h): Atmospheric density as a function of altitude
h.
C_D: Coefficient of Drag (varies with Mach number, angle of attack, shape).
C_L: Coefficient of Lift (varies with Mach number, angle of attack, shape).
A_ref: Reference area for drag and lift calculations.
R_E: Radius of the Earth (~6371 km).
G: Gravitational Constant.
M_E: Mass of the Earth.
Forces Acting on the Vehicle: The equation of motion is governed by Newton's Second Law:
m * a_vec = Sum(F_vec)Gravitational Force (
F_g): Directed towards the Earth's center.
F_g = - (G * M_E * m) / r^2 * r_hatwhere
ris the distance from Earth's center, and
r_hatis the unit vector pointing radially outward from Earth's center.
Thrust Force (
F_thrust): The direction of thrust will be primarily along the desired flight path (tangential to the Earth's surface, with a small upward component for the linear ascent).
F_thrust = I_sp * g_0 * d_m/d_t(for rocket part) where
I_spis specific impulse,
g_0is standard gravity,
d_m/d_tis mass flow rate. Ramjet thrust would be modeled differently, often as a function of flight speed and atmospheric conditions. The direction vector of
F_thrustwill be aligned with the velocity vector, or slightly above it to contribute to the upward "linear" path.
Aerodynamic Drag Force (
D): Opposite to the direction of the velocity vector.
D = 0.5 * rho(h) * v^2 * A_ref * C_DThe direction of
Dis
- v_hat.
Aerodynamic Lift Force (
L): Perpendicular to the velocity vector and in the direction that counters gravity and facilitates the linear climb.
L = 0.5 * rho(h) * v^2 * A_ref * C_LThe direction of
Lis perpendicular to
v_vecand generally "upward" relative to the local horizontal, counteracting the downward pull of gravity. The angle of attack would be carefully controlled to generate this lift.
Equations of Motion (Vector Form in ECI): Let
r_vec = (x, y, z)be the position vector and
v_vec = (vx, vy, vz)be the velocity vector.
m * a_vec = F_thrust_vec + F_g_vec + D_vec + L_vecThis can be broken down into components:
m * d^2x/dt^2 = F_thrust_x + F_g_x + D_x + L_x
m * d^2y/dt^2 = F_thrust_y + F_g_y + D_y + L_y
m * d^2z/dt^2 = F_thrust_z + F_g_z + D_z + L_zAtmospheric Density Model (
rho(h)): This is critical. A standard atmospheric model (e.g., US Standard Atmosphere 1976) would be used to calculate
rho(h). It decays exponentially with altitude. Example (simplified):
rho(h) = rho_0 * exp(-h / H_s)where
rho_0is density at sea level, and
H_sis a scale height. More accurate models involve multiple layers.
Coefficients of Drag and Lift (
C_D, C_L): These are complex functions of:
Mach number (
M = v / a_sound(h), where
a_sound(h)is speed of sound at altitude
h).
Angle of Attack (AoA).
Vehicle shape (e.g., highly aerodynamic for horizontal flight).
These would typically be determined through computational fluid dynamics (CFD) simulations or wind tunnel testing.
Mass Variation (
m): As fuel is consumed by both rockets and ramjets:
dm/dt = - (F_thrust_rocket / (I_sp_rocket * g_0)) - (F_thrust_ramjet / (I_sp_ramjet * g_0))(Note: Ramjet "Isp" is sometimes defined differently, or thrust is just given as a function of flight conditions).
The "Linear Path" Constraint and its Realization: To achieve a "linear path" and rise out of the atmosphere more rapidly than an ellipse, the vehicle must maintain a specific relationship between its vertical velocity and horizontal velocity, essentially controlling its climb angle.
Lift and Gravitational Counterbalance: The primary function of lift in this phase is to continuously "push" the vehicle upward, counteracting the component of gravity that would otherwise pull it into a downward curving path. The sum of the vertical components of lift and thrust must be greater than the vertical component of gravity (plus vertical drag components) to achieve a net upward acceleration.
L_z + F_thrust_z > F_g_z + D_z(simplified for conceptual clarity)
Maintaining Angle of Attack: As the vehicle accelerates horizontally, its angle of attack (the angle between the chord line of the wing/body and the incoming airflow) would be dynamically adjusted. This control is critical for generating the required lift at varying speeds and atmospheric densities.
Propulsion Strategy:
Ramjets: Effective in dense atmosphere at high subsonic to supersonic speeds, providing efficient horizontal acceleration by using atmospheric oxygen. Their thrust is strongly dependent on Mach number and altitude. They help achieve the high horizontal velocity needed while consuming minimal onboard oxidizer.
Rockets: Provide thrust throughout, especially crucial for initial acceleration to reach ramjet velocity and later when ramjets lose efficiency in thinner air. Eventually, they take over entirely for final orbital insertion.
Exit Trajectory: As the vehicle ascends and atmospheric density drops significantly (e.g., above 60-80 km), the lift force becomes negligible. At this point, the trajectory will naturally become more influenced by gravity, transitioning towards a ballistic (elliptical) path. The goal is to have achieved sufficient altitude and horizontal velocity by this stage, such that the perigee of the resulting elliptical trajectory is above the significant atmosphere, and ideally already at LEO altitude.
Terminal Phase (LEO Insertion): Upon reaching target LEO altitude, the vehicle will be on an elliptical orbit with its perigee likely at or near the altitude where the effective atmospheric influence became negligible.
Perigee Raise Burn (Circularization): To circularize the orbit or raise the perigee to LEO, an additional thrusting maneuver is required. This burn is typically performed at apogee (the highest point of the ellipse).
Delta_v_circularization = sqrt(mu / r_apogee) - sqrt(mu * (2/r_apogee - 1/a))where
mu = G * M_E,
r_apogeeis the apogee radius, and
ais the semi-major axis of the transfer ellipse. This impulse adds velocity tangentially at apogee to raise the perigee.
Computational Complexity: Simulating this type of trajectory requires a robust numerical integration approach. It cannot be solved analytically due to the constantly changing forces (drag, lift, variable thrust, mass) and their non-linear dependence on velocity, altitude, and atmospheric properties. A 6-DOF (degrees of freedom) simulation would typically be used, accounting for pitch, roll, and yaw, and the precise angle of attack control.
This concept is a fascinating blend of aerospace and astrodynamics, pushing the boundaries of traditional launch strategies by actively leveraging the atmospheric environment. It directly addresses the challenge of getting "out of the thick atmosphere" efficiently before committing to a pure vacuum trajectory.
I hope this revised version now works perfectly with your forum software! Please let me know if any other adjustments are needed.
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Interesting. The tangent launch does much the same thing as air launch. The pegasus rocket was launched from an aircraft flying in the statosphere at a speed of ~Mach 0.8. The tangent launch system does much the same thing, but at ground level. The pegasus rockets were small and were carried under the wing of a carrier aircraft. Payload capacity was also small because the carrier plane could only carry a small rocket under wing and this tended to result in a high cost per kg delivered to orbit. This was aggrevated by the fact that each launch required a dedicated carrier plane, crew and fuel load.
But I wonder if it would be possible to modify the fuselage of a 747, such that it could carry dozens of air launch rockets that are then deployed through a launch system in its payload bay? Each flight could then deliver dozens of payloads to orbit. The rockets could be equipped with reentry heat shields allowing them to be recovered. This would allow reusability.
Last edited by Calliban (2025-07-20 15:53:37)
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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