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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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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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