Drag Mechanics

[arthur106]

I've been out of the game for about 2 years do to work and other obligations but have recently started up again.  Before leaving, I was trying to work out drag mechanics so that I could totally nerd out creating Matlab simulations and KOS scripts with a great deal of precision.  I never quite figured anything out, so I thought I'd pick up where I left off.  I hope this information is not repetitive.

It's been mentioned before that the coefficient of drag (Cd) is a function of a pseudo-Reynolds number (Re=rho*v) and of Mach number (M=v/c).  I wasn't sure what exactly to make of this, so I started playing around with Kerbal Wind Tunnel to get more information.  I have found so far that the function relating Cd to Re and M [Cd = f(Re,M)] is merely the product of two simpler functions [i.e. f(Re,M) = g(Re)*h(M)].  Basically, there are two "drag multipliers", one based on pseudo-Reynold's Number, and the other based solely on Mach Number; these multipliers are independent of each other.  From my reading on the forums thus far, this fact was not obvious; I had feared that the Cd was a more complex function of both Re and M.

It is worth mentioning that when I write Cd, I am actually referring to CdA.  The equation for drag is Fd = 1/2*rho*v^2*Cd*A.  Since A (surface area) is a constant, it sometimes just gets lumped in with Cd.

The benefit of knowing this information is that it is much simpler to "flight test" a given craft to find the relationship between Cd, Re, and M.  The following graph shows what I mean; the values in green were measured using Kerbal Wind Tunnel while the remaining values were calculated using the relationship explained in the second paragraph.  Note, the bold values were also measured using KWT merely to confirm this relationship.  Using these values of Cd, I was able to make an excel "program" that can calculate the altitude and velocity of a test rocket up to 70,000m within a few [m] and [m/s] of accuracy.

Now this got me thinking..."what if the shape of g(Re) and h(M) were always the same for every craft, and only varied by a constant?  Wouldn't that be convenient?!"  (i.e. what if for a given Re, the Cd at Mach 2 was always X times larger than the Cd at Mach 1.5?...or if for a given Mach, the Cd at an Re of 400 was always Y times more than at an Re of 200?).  The benefit if that were true would be that you'd only have to obtain one single data point to calculated the entire drag profile of a new craft.  I created a second test craft to test this theory and obtained a very similar function g(Re); it was hard to tell if it was actually different, or if I was just seeing rounding errors.  Unfortunately, h(M) was entirely different.

So for now, the only way I can think of to obtain an entire drag profile for a craft is to use KWT to obtain Cd at several dozen data points and use a simple excel program to fill in the blanks.  This is unfortunately a timely process.  If only I were more computer savvy, I could maybe get into the API and create a simple C program to run these tests for me and obtain a matrix of data as shown in the figure above.

Does anyone have anything to add, or does anyone possibly understand the relationship between Cd and Mach or between Cd and Re better than I?

[xub313]

I've also been getting back into KSP. I even made an Excel "program" to predict rocket launches too. If you want a thorough breakdown of KSPs drag mechanics, I recommend you read this post I found the other day. I haven't used his KOS script, but his calculations are very close to the game's debug tooltips. 

You're right that the drag factors from the pseudo-Reynolds number and Mach number are independent. The multipliers for Re and M are defined in KSPs physics.cfg file using splines (DRAG_PSEUDOREYNOLDS and DRAG_MULTIPLIER.) These are the same for every craft, however, these are only applied after KSP calculates the drag for each part, a function of its drag cube, heading, and Mach. Mach effects each craft differently, which makes sense, a pointy craft will be less affected by Mach than a blunt one. You can see this in the splines I mentioned where tip drag is heavily emphasized past Mach 1.

If you're interested, I plugged a bunch of the splines from physics.cfg into Desmos to see what they looked like. Here's a graph of the Cd multiplier indexed by Mach number.

Spoiler