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What is the relationship between dynamic pressure and aerodynamic force?

Question

So I have been trying to model the physics in KSP for a while, using kRPC. I am trying to compute the air drag acting on my rocket so I can compute the trajectory. The kRPC states that the dynamic pressure is a measure of the strength of the aerodynamic forces (link) and the formula is 0.5 * air density * velocity2. Now the KSP wiki states that the atmospheric drag follows the same fomula with an extra constant (coefficient of drag * cross-sectional area). Hence I assumed that when I fly my rocker straight up, where the aerodynamic forces is basicly air drag downwards (numericly checked), the dynamic pressure would be linear to the aerodynamic force. But the experiment shows the other way, as the following figure depicts, where Q is the dynamic pressure. So aerodynamic force is firstly near linear with repect to Q, then as Q hits 40000, is negatively linear and then follows this strange curve. After max Q, it's near linear again.

Dynamic pressure data is acquired by vessel.flight().dynamic_pressure, while aerodynamic force data is acquired by norm(vessel.flight().aerodynamic_force).

Can anyone share what is the relationship between dynamic pressure and aerodynamic force?

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Posted (edited)
1 hour ago, Npa said:

Can anyone share what is the relationship between dynamic pressure and aerodynamic force?

Some of many components of aerodynamic force that acts on each part scale linearly with dynamic pressure.

You can safely abandon the idea of trying to look for a simple formula for your task. There is none.

If you want to see what's happening under the hood, consult KerbalWindTunnel or CorrectCoL mod sources.

Edited by Boris-Barboris

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Posted (edited)

Drag coefficient is a function of Mach number.  It peaks around Mach 1.

How KSP computes drag is complex.  It's by no means as simple as taking a drag coefficient times the cross-sectional area.  As I understand it, each part has a "drag cube" with each face having an area and a drag coefficient.  How much each face contributes to the drag depends on its exposure to the wind.  There are different multipliers applied depending on whether the face is a tip, surface or tail.  Then, of course, there is a Mach number multiplier.  The drag from all the parts is added up to give the total drag.

I don't think there's really anyway to compute it yourself.  The closest that I've come is to empirically estimate an overall drag coefficient.  But that's only a ballpark.

Edited by OhioBob

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20 minutes ago, Boris-Barboris said:

Some of many components of aerodynamic force that acts on each part scale linearly with dynamic pressure.

You can safely abandon the idea of trying to look for a simple formula for your task. There is none.

If you want to see what's happening under the hood, consult KerbalWindTunnel or CorrectCoL mod sources.

Thanks! I will check those.

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Posted (edited)
1 hour ago, OhioBob said:

Drag coefficient is a function of Mach number.  It peaks around Mach 1.

How KSP computes drag is complex.  It's by no means as simple as taking a drag coefficient times the cross-sectional area.  As I understand it, each part has a "drag cube" with each face having an area and a drag coefficient.  How much each face contributes to the drag depends on its exposure to the wind.  There are different multipliers applied depending on whether the face is a tip, surface or tail.  Then, of course, there is a Mach number multiplier.  The drag from all the parts is added up to give the total drag.

I don't think there's really anyway to compute it yourself.  The closest that I've come is to empirically estimate an overall drag coefficient.  But that's only a ballpark.

Drag coefficient is a function of Mach number! I missed that.

Indeed, now I know (and truely appreciate) how complex aerodynamics is. As @Boris-Barboris suggested, KerbalWindTunnel seems a good mod where I can compute the aerodynamics of my vessel. The mod supports outputing the aerodynamic profile as a csv file. I think I can then take your idea, like using a polynomial function to empirically estimate the drag or just use the csv file as a lookup table to get a drag value? Damn, talk about doing science! This feels great.

P.S. I've just started trying to look under the hood, I know some of my questions might be rather stupid. Really greatful for you guys replying and helping me out!

Edited by Npa

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Posted (edited)
1 hour ago, Npa said:

I think I can then take your idea, like using a polynomial function to empirically estimate the drag or just use the csv file as a lookup table to get a drag value? Damn, talk about doing science! This feels great.

Sounds like a good plan.  When I played around with this, I didn't know about KerbalWindTunnel (not sure if it existed at the time).  I estimated the drag coefficient by using the AeroGUI from the cheat menu to periodically record dynamic pressure, drag, and Mach number throughout a launch.  I could then calculate the drag coefficient and plot it vs. Mach number.  Your way sounds easier.

Something else that complicates things is that the Cd is also sensitive to angle of attack.

I was working on a page for my website that explains all about drag and drag coefficients as it relates to rockets.  It's still a work in progress so it's not published yet.  I think everything dealing with launch vehicles is finished, the unfinished part deals with blunt body reentry vehicles.  Perhaps I can make available to you what I've written so far if you think it would be helpful.

(edit)

Here's my incomplete paper.  I've deleted the stuff that's still a work in progress.  I don't guarantee that all the links work.

Edited by OhioBob

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12 hours ago, OhioBob said:

Here's my incomplete paper.  I've deleted the stuff that's still a work in progress.  I don't guarantee that all the links work.

Just had a quick scan, very informative! And I think the other content in your website would also help me learning rocket science a lot. Thanks!

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