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For SpaceNut ...
We did not have a topic about drag in the Science, Technology and Astronomy Category.
The subject is fundamental to space transportation as well as ordinary atmosphere transportation.
It is also fundamental to all wind energy technology.
This topic is available for NewMars members who might wish to contribute links, images or text on the subject.
We'll open Post #3 with a summary worked up by Google ... There is much more to be added.
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Index:
Post #3: An opening summary by Google
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This is a summary worked up by Google to start off this new topic:
Opening question: how do cannon designers account for drag against projectiles. Drag must increase with velocity. What is the increase ratio?
Cannon designers account for drag through extensive ballistic modeling and design optimization, incorporating the drag force directly into trajectory calculations.
For high-velocity cannon projectiles, the drag force increases approximately with the square of the velocity (\(v^{2}\)). How designers account for drag Ballistic calculations and modeling
Since at high speeds drag is a dominant force, designers calculate a projectile's trajectory using the full drag equation, rather than a simple, no-drag parabolic path. This mathematical model must account for the following factors to accurately predict the projectile's flight path:
Air density: Density changes with altitude, which affects the drag force.
Drag coefficient (\(C_{d}\)): A dimensionless number that accounts for the projectile's shape and surface characteristics. It is not a constant, especially for objects moving near or faster than the speed of sound (Mach 1).
Cross-sectional area: The projectile's frontal area, which pushes against the air.
Velocity: The projectile's speed, which is the most significant factor affecting drag.
Projectile design Drag is heavily influenced by the projectile's shape. Modern cannon projectiles are designed to be aerodynamic to minimize drag and maintain stability during flight. Streamlined shape: Modern artillery shells have pointed, streamlined noses that reduce the pressure drag caused by moving air out of the projectile's path.
Fins and grooves: Features like fins on rockets or the spin imparted by rifling in cannon barrels help to stabilize the projectile and maintain a predictable trajectory.
Ballistic coefficient: Designers use this metric to indicate a projectile's ability to overcome air resistance. A higher ballistic coefficient signifies less drag. High-speed complexities For cannon projectiles that travel at supersonic speeds, drag is more complex and harder to model accurately.
Variable drag coefficient: Around the speed of sound, the drag coefficient (\(C_{d}\)) changes significantly due to the formation of shockwaves.
A simple quadratic relationship for drag is not sufficient for high velocities.
Experimental data: Designers rely on wind tunnel experiments and data from live-fire tests to create empirically derived drag models that account for the non-linear changes in drag at supersonic speeds.
The velocity increase ratio
For high-velocity objects like cannon projectiles, the drag force increases with the square of the velocity.
The drag equation is given by:
\(F_{d}=\frac{1}{2}\rho C_{d}Av^{2}\)
Where: \(F_{d}\) is the drag force.
\(\rho \) is the density of the fluid (air).
\(C_{d}\) is the drag coefficient.\(A\) is the cross-sectional area.
\(v\) is the projectile's velocity.This means that if a projectile's velocity doubles, the drag force will quadruple.
This quadratic relationship is the primary reason why high-velocity projectiles lose speed so rapidly compared to slower objects and why designers must so carefully engineer the projectile's shape and account for drag in their calculations.
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This part of a rockets landing equations where the molecular content with the amount of resistance to movement and changes heat build up due to the friction that an atmoshere.
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Spacenut:
Here is a link to a sketch I drew showing how the drag and the heating vary for high speed flight in the atmosphere, getting into hypersonics, as you approach orbital-class speeds.
http://40.75.112.55/phpBB3/download/file.php?id=7
The hypersonic heating is best done by simplified correlations for stagnation point heating, and scaled to other locations by means of experimental data. The oldest and simplest of those stagnation point convective heating correlations is the one used by H. Julian Allen for warhead entry in the early 1950's: Q/A = constant * sqrt[density/nose radius]*[velocity^3]. Plasma radiation heating is somewhat similar, but has a much higher exponent on velocity.
The image showing where ionization starts "kicking in" shows about Mach 6. It gets to be more than a 10% error in estimated temperature at about Mach 7.
Hope that helps.
GW
Last edited by GW Johnson (2025-09-01 07:49:06)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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This post contains an attempt by Gemini (2.5) to estimate the drag for a projectile at 11 km/s.
Drag Force Calculation
The drag force (F[sub]D[/sub]) on a projectile is calculated using the following equation:
F[sub]D[/sub] = 1/2 * ρ * v[sup]2[/sup] * A * C[sub]D[/sub]
Where:
ρ (rho) is the density of the fluid (air).
v is the projectile's velocity.
A is the reference area (the cross-sectional area).
C[sub]D[/sub] is the drag coefficient.
Estimated Drag for the Projectile
Air Density (ρ): We used the standard density of air at sea level, which is approximately 1.225 kg/m[sup]3[/sup].
Velocity (v): The velocity is 11 km/s, or 11,000 m/s.
Reference Area (A): With a diameter of 1 meter, the cross-sectional area is approximately 0.785 m[sup]2[/sup].
Drag Coefficient (C[sub]D[/sub]): For a sharp cone at these hypersonic speeds, we estimated a value of 0.2. This is a conservative figure, as the flat bottom would significantly increase this number.
Final Computation
F[sub]D[/sub] = 1/2 * (1.225 kg/m[sup]3[/sup]) * (11,000 m/s)[sup]2[/sup] * (0.785 m[sup]2[/sup]) * (0.2)
F[sub]D[/sub] ≈ 11,540,000 Newtons
This means the projectile would experience a drag force of approximately 11.5 meganewtons. This is a powerful force, equivalent to the weight of over 1,170 metric tons, and it highlights the immense challenges of hypersonic flight at sea level. The flat bottom would significantly increase this drag due to the creation of a low-pressure wake, a phenomenon known as base drag
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Quick note from GW Johnson via email:
Drag force is then coefficient times area times dynamic pressure (quadratic with speed, linear with density). That's spreadsheet stuff.
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its why going with a large heat shield diameter for mars is favored for getting more to the surface of mars as mass also plays into the equation.
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For SpaceNut re #8 .... thanks for your note on the heat shield for the thin atmosphere of Mars. In that case, the mass of the air is less than for Earth, so the relationship is linear.
Here is an attempt by Gemini to explain the relationship articulated by GW Johnson in Post #7:
The Physics of Drag: A Kinetic Energy Story
Imagine a wing flying through the air. As it moves, it has to push air molecules out of the way. The drag force it experiences is basically the "push back" from all those molecules. The faster the wing moves, two things happen:
More air molecules are pushed out of the way each second. The amount of air mass (m) you encounter is directly proportional to your speed (v). Double your speed, and you'll run into twice as many air molecules in the same amount of time.
You push each molecule with more force. The speed you impart to those air molecules is also proportional to your own speed (v).
Drag force (FD) is a direct result of these two effects. Because both the amount of air and the push you give it are linked to your speed, the relationship becomes squared.
More air molecules to push (proportional to v)
You push them harder (proportional to v)
The total force is the product of these two effects (FD is proportional to v x v = _v_²)
This is why doubling your speed doesn't just double your drag; it quadruples it!
Key Formulas and Their Meanings
Here are the formulas and a list of what the symbols mean. The formulas themselves are written in a way that should work with basic text formatting.
Drag Force (FD) Formula
F_D = 1/2 * p * v^2 * C_D * ALift Force (FL) Formula
F_L = 1/2 * p * v^2 * C_L * AList of Symbols:
FD: Drag Force (the force resisting motion)
FL: Lift Force (the force pushing an object up)
p (rho): Density of the fluid (for a wing, it's the density of the air)
v: Velocity (speed) of the object
CD: Coefficient of Drag (a number that describes how "slippery" or aerodynamic a shape is)
CL: Coefficient of Lift (a number that describes how much lift a shape generates)
A: Reference Area (for a wing, this is the planform area of the wing)
The part of the explanation that worked for me was showing that v appears twice, which explains the quadratic relationship.
More air molecules to push (proportional to v)
You push them harder (proportional to v)
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