Falcon 9 velocity/altitude values from webcast

[Semmel]

Got my smoothing function back and applied it on some of the data, not to improve the initial interpolation though.

I updated the flight data plot with some annotations. Its very interesting what you can see in the data, especially the acceleration. You can clearly see the Max Q throttle and of course MECO and the ignittion of the second stage. Less clearly but still good enough, one can see the fairing separation and also a throttle back of the M1D at around 300s. I have not heard about that one before.

Unfortunately, my atmosphere model still seems grossly wrong. I assume I have some units wrong, will investigate when I have time.

I also added a plot to show the velocity components in vertical and horizontal direction. Its very nice to see how the F9 launches vertically and ends up thrusting horizontal. I tried to get acceleration data from these as well but due to the nature of data gathering (brilliant as it is done), the interpolation fragments dominate the plots and you cant see what is going on any more.

I will be back with more computations when I have time

[S.Paulissen]

That's awesome Semmel.  I, too, caught the second stage throttle in your previous graph you made but did not comment on it.  Your new graph is clearly superior as I did not notice the fairing separation at all.  Great work!

When I saw the acceleration curves the other day, it made me wonder if we could suss out a more definite mass of the fairing and second stage based on the change of acceleration from staging events.

[Semmel]

That's awesome Semmel.  I, too, caught the second stage throttle in your previous graph you made but did not comment on it.  Your new graph is clearly superior as I did not notice the fairing separation at all.  Great work!

When I saw the acceleration curves the other day, it made me wonder if we could suss out a more definite mass of the fairing and second stage based on the change of acceleration from staging events.

Hi Paulissen,

yes, estimating the mass of the fairing should definitely be possible. I will work on that tomorrow maybe if family life allows it ;-) Currently I am trying to align my atmospheric model (its getting more complex every time I touch it!) with the throttle back of the first stage. The reason for this is, if I have the correct drag force on F9, I can use the mass (initial mass is known), the acceleration and drag force to compute the thrust of F9. That way, I can compute the throttle setting of F9 when it throttles back for max Q. Currently that is not possible because I cant get the dynamic pressure to work. If anyone has a suggestion of what is wrong, please let me know!

Input:
h    # height of falcon in [m]
v    # velocity of falcon in [m/s]

# some constants
T_0 = 288.15        # Sealevel standard temperatur [K]
p_0 = 101325        # Sealevel pressure [Pa]
h_0 = 8435          # Scale Factor for air pressure [m]
R = 8.31447         # ideal gas constant [J/(mol*K)]
g = 9.80665         # earth gravity [m/s^2]
L = 0.0065          # temperature lapse [kg/m]
M = 0.0289644       # molar mass of air [kg/mol]
mach_peak = 1.1     # assumed mach number for which the drag peaks
gamma = 1.4         # adiabatic index of air. Estimation.

# Falcon 9
A = (0.5 * 5.2)**2 * np.pi  # cross section area in [m^2]
C_0 = 0.07         # drag constant value at speed far below mach1

# Standard atmosphere
std_atm_h = [   0.0, 11000.00, 20000.00, 32000.00, 47000.00, 51000.00, 71000.00, 500000.00]
std_atm_T = [288.15,   216.65,   216.65,   288.65,   270.65,   270.65,   214.65,    214.65]
atm_T = sc.interpolate.interp1d(std_atm_h, std_atm_T, kind='linear')

# Temperature at hight values
T = atm_T(h)

# air pressure depending on hight
p = p_0 * np.exp(- g * M * h / (R * T_0))

# air density depending on pressure and temperature
rho = p * M / (R * T)

# mach depending on pressure and air density
# https://en.wikipedia.org/wiki/Speed_of_sound#Speed_of_sound_in_ideal_gases_and_air
mach_1 = np.sqrt(gamma * R * T / M)
mach = v / mach_1

# Drag coefficient model depending on mach number, following this approximation: http://home.myfairpoint.net/tfr001/atmos3.htm
C_d = C_0 * np.power(300.0, -(mach_peak - mach)**2) + 0.01 * mach + C_0

# drag computation taken from https://de.wikipedia.org/wiki/Luftdruck#Variabilit.C3.A4t_und_Extremwerte
F_drag = 0.5 * rho * v**2 * C_d * A
p_dyn = 0.5 * rho * v**2

There is not much that can be wrong to fix the values. If the model is correct but some values are wrong, there is not much that can be fixed.
For max drag, only rho can be wrong. So if rho is wrong, it can only be because of the pressure p or temperature T, the other stuff is just physics. I tried to fudge the temperature to align the values and the resulting temperatures are rediculus. So its not T. Leaves the pressure p. Since maxQ is a product of pressure and velocity squared, it is not enough to change the scale of p, as it would only affect the hight of the curve, not the location of its maximum. So the pressure equation needs to be adjusted inside the exponent. I figured,
p = p_0 * np.exp(- 1.75 * g * M * h / (R * T_0))
gives a reasonable lineup. That factor of 1.75 is rediculus, I dont think that such an error can happen inside there. Maybe velocity and height are seriously out of sync in the telemetry data, but that is pretty unlikely I would say. I am at a loss here. Any suggestion would be wonderful!

[DAZ]

Trans sonic drag and lack of area rule shape?

[IainMcClatchie]

This is awesome work.  Are you writing the code in Python?  What graphing package are you using?

You might try checking your atmosphere against the NASA standard atmosphere of 1976.  You can test individual points with this online calculator, or you can just use the model here.

[nicp]

If I read that correctly the cross-sectional area for the Falcon assumes a diameter of 5.2m - its less than 4 isn't it?
Great stuff...

EDIT: Oh, 5.2m is the fairing diameter of course..

[moralec]

This thread really shows how awesome NSF is! Amazing work!

[Proponent]

C_0 = 0.07         # drag constant value at speed far below mach1

Seems awfully low to me.  Attached is a paper on the aerodynamics of the Block I Saturn I.  While I wouldn't expect it to be a close match to the Falcon 9, I would have thought it would agree in order of magnitude.  Have a look, for example, at the plot of the axial-force coefficient on page 31 of the PDF, which I believe is the same as the drag coefficient at zero angle of attack.

[Herb Schaltegger]

Drag coefficient for an ogive-shaped fairing and long cylinder should be pretty easy to find in some basic aerodynamic texts and/or AIAA papers. This may not allow for easy internet research, but that kind of thing has been methodically studied by NACA/NASA since at least the 1930's.

[Space Opera]

My own MaxQ calculation show roughly similar results.
The most probable is that our numbers are wrong, but is it possible that the throttle decreases before MaxQ ? Because clearly my curves show that the loss of acceleration seconds before MaxQ leads to a significant lower MaxQ than if the throttle was keep constant.

[ugordan]

The most probable is that our numbers are wrong, but is it possible that the throttle is decrease before MaxQ ?

I think they may actually be throttling down for the supersonic/transonic regime buffeting. John Insprucker sort of hinted at that in a few webcasts, IIRC. If you compare to the velocity plot, it seems to be around Mach 1.

[Herb Schaltegger]

The most probable is that our numbers are wrong, but is it possible that the throttle is decrease before MaxQ ?

I think they may actually be throttling down for the supersonic/transonic regime buffeting. John Insprucker sort of hinted at that in a few webcasts, IIRC. If you compare to the velocity plot, it seems to be around Mach 1.

Indeed. And MaxQ is typically right around Mach 1, though rarely if ever exactly at that point. It varies from vehicle to vehicle, T/W ratio, ascent profile, etc.

[ugordan]

I know, I was just pointing out that the throttle down doesn't appear to match max Q which for F9 occurs several seconds after going supersonic. I think I remember only one instance where maxQ was called out *before* supersonic, it might have been the Orion Delta IV Heavy launch.

[Semmel]

This is awesome work.  Are you writing the code in Python?  What graphing package are you using?

You might try checking your atmosphere against the NASA standard atmosphere of 1976.  You can test individual points with this online calculator, or you can just use the model here.

Yes, I use python and the matplotlib package. I checked pressure values against lists online and they are pretty good. Only very minor deviation. Also, I use the standard atmosphere model for the temperature vs. altitude approximation.

Drag coefficient for an ogive-shaped fairing and long cylinder should be pretty easy to find in some basic aerodynamic texts and/or AIAA papers. This may not allow for easy internet research, but that kind of thing has been methodically studied by NACA/NASA since at least the 1930's.

I guestimated there. The most stuff I found on drag coefficients is for unpropelled objects. If the engines of the F9 wouldnt run, it would have something in the order of 0.2 or 0.25. An airfoil has something below 0.05, so I went for a small number in the middle. The Saturn 5 is nice and all, but it has rather awkward shape and it had fins at the base, which increase Cd quite a lot. Nevertheless, I have an alternative plan how to find out.. Not telling you in case it is utter nonsense and I dont want to embarrass my self ;-)

My own MaxQ calculation show roughly similar results.
The most probable is that our numbers are wrong, but is it possible that the throttle decreases before MaxQ ? Because clearly my curves show that the loss of acceleration seconds before MaxQ leads to a significant lower MaxQ than if the throttle was keep constant.

Well, I count on our numbers being wrong for now. But I have an alternative plan.. needs time though that I currently dont have. The data is not running away, I will get to it eventually.

The most probable is that our numbers are wrong, but is it possible that the throttle is decrease before MaxQ ?

I think they may actually be throttling down for the supersonic/transonic regime buffeting. John Insprucker sort of hinted at that in a few webcasts, IIRC. If you compare to the velocity plot, it seems to be around Mach 1.

Quite possible. Actually an interesting proposal. I added the region of mach 0.9 to 1.2 to the plot. Not an exact fit but quite close. Interesting interesting interesting.

[ugordan]

Quite possible. Actually an interesting proposal. I added the region of mach 0.9 to 1.2 to the plot. Not an exact fit but quite close. Interesting interesting interesting.

Does that take into account the lower speed of sound at that altitude (10-ish km)? I think Mach 1 might be around 300 m/s or thereabouts there.

[Semmel]

Quite possible. Actually an interesting proposal. I added the region of mach 0.9 to 1.2 to the plot. Not an exact fit but quite close. Interesting interesting interesting.

Does that take into account the lower speed of sound at that altitude (10-ish km)? I think Mach 1 might be around 300 m/s or thereabouts there.

Yes. Here a short list

h [m]	mach	speed of sound [m/s]
6991	0.9	312
8052	1.01	308
9512	1.18	301

[IntoTheVoid]

# air pressure depending on hight
p = p_0 * np.exp(- g * M * h / (R * T_0))

# air density depending on pressure and temperature
rho = p * M / (R * T)

From https://en.wikipedia.org/wiki/Density_of_air:
I see the formula below, and while yours has some similar features, I don't see the equivalence. (Though I'll admit that could be my own ignorance. )
Not sure why you're using eⁿ, have h in the exponent, and not using L.

[Semmel]

I took this equation since its a bit simpler:



https://en.wikipedia.org/wiki/Atmospheric_pressure#Altitude_variation

You find this equation not only on wikipedia, also many other sites use that form. I dont think the approximation can be responsible for the differences we see. It wouldnt be a well accepted one if that was the case.

[Proponent]

The Saturn 5 is nice and all, but it has rather awkward shape and it had fins at the base, which increase Cd quite a lot.

The data posted apply to the Block I Saturn I, which had no fins, though I do realize now that I had confused C_0 with Cd, so the discrepancy with the Saturn I is not nearly as large as I had thought.

[Proponent]

I took this equation since its a bit simpler:



https://en.wikipedia.org/wiki/Atmospheric_pressure#Altitude_variation

You find this equation not only on wikipedia, also many other sites use that form. I dont think the approximation can be responsible for the differences we see. It wouldnt be a well accepted one if that was the case.

That equation assumes the temperature is constant.  Standard atmosphere models usually divide the atmosphere into regions, some of which are isothermal and some of which have linear temperature gradients.  A suggestion for a quick-and-easy tweak: use an isothermal model optimized for the altitude at which max Q drag occurs.