What is Velocity.length_squared?

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SUMMARY

The discussion centers on calculating the velocity of an asteroid as it enters Earth's atmosphere, specifically focusing on the concept of terminal velocity and the effects of ablation. Participants emphasize the importance of applying Newton's laws of motion and understanding the forces acting on the asteroid, including gravity and drag. Key equations mentioned include the drag equation F_d = \frac{1}{2} \rho v^2 C_d A and the gravitational force equation F = \frac{GMm}{r^2}. The conversation highlights the complexities of modeling these physical phenomena accurately, particularly for a beginner-level physics project.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with the drag equation and its components
  • Basic knowledge of gravitational forces and their calculations
  • Concept of ablation and its impact on velocity
NEXT STEPS
  • Research the International Standard Atmosphere model for air density variations with altitude
  • Learn about the conservation of energy in relation to ablation and velocity changes
  • Study the effects of drag coefficients on falling objects
  • Explore numerical methods for simulating motion in physics programming
USEFUL FOR

This discussion is beneficial for students and educators in physics, particularly those involved in projects related to motion simulation and atmospheric entry dynamics. It is also valuable for programmers developing simulations that require accurate physical modeling.

  • #31
Amsalja said:
And is that the average?
Average what? The physics model calculates the instantaneous speed at each point in time.
Amsalja said:
If it is then all I need is the ablation.
That's easy to say, but meteoroid ablation is a really complicated subject that is not fully understood. Even a basic study in this area would be at the level of a final year project for an undergraduate. Also, most of the relevant texts are not freely available on the internet: you would need access to a university library for this.

Having said that, this paper quotes an equation for the ablation rate (quoted from V. A. Bronshten, Physics of Meteoric Phenomena, Reidel Publishing Co., Dordrecht, Netherlands, 1983)
$$ \frac{dm}{dt} = -\sigma K \rho_{air} m^{2/3} v^3 $$
where σ and K are constants. The paper also provides some values for σ between = 0.035 and 0.081 s2km-2, and another expression that after a bit of work gives ## Km^{2/3} = \frac 1 2 C_D A ##, so the equation above becomes
$$ \frac{dm}{dt} = - \frac 1 2 \sigma C_D A \rho_{air} v^3 = \sigma F_D v $$
I'm not sure this makes sense, but taking it at face value and coding it we have:

[code lang=Python title=GDScript]
# sigma is an input parameter in the range 0.035 - 0.081 s^2 km^{-2}
# so we need to convert to s^2 m^{-2}
convertedSigma = sigma / 1000000
# From the calculations at
# https://www.physicsforums.com/threads/7th-grade-asteroid-simulator.1053384/post-6908342
# we can update mass
mass -= convertedSigma * dragForceMagnitude * speed * delta
[/code]

Amsalja said:
Another thing, is drag is able to go below terminal velocity and I know that you said not to talk about terminal velocity, but, if I start my velocity at my terminal velocity, then I fall in, the velocity goes below it's terminal velocity due to drag, so does that mean my drag is wrong?
Yes there was an error in the code I posted: the calculation of the amount of deceleration due to drag was correct, but when converting this to a vector to get it in the right direction I forgot to use a unit vector. The correction is below, I have amended this in the post above:
[code lang=Python title=GDScript]
# Aerodynamic drag depends on speed squared...
speedSquared = Velocity.length_squared()
dragForceMagnitude = 0.5 * airDensity * speedSquared * dragCoefficient * crossSectionArea
# ...and acts in the opposite direction to the velocity so we create a vector,
# remembering to scale Velocity to a unit vector.
speed = sqrt(speedSquared)
DragForce = -dragForceMagnitude * Velocity / speed
[/QUOTE][/CODE]
 
Last edited:
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  • #32
What is Velocity.length_squared? Is it the length axis, or is it something else.
 

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