Orbiter-Forum [Tutorial] Selecting the correct altitude for a given peak hull temp with the Ravenstar.
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#1
 dgatsoulis ele2png user
Selecting the correct altitude for a given peak hull temp with the Ravenstar.
by dgatsoulis 06-18-2014, 08:19 PM

Before we start I'd like to thank Douglas E. Beachy and Steve "Coolhand" Tyler for creating one of the most amazing and fun to fly spacecrafts in Orbiter. Also an additional thanks to Doug for sharing a part of the Ravenstar's hull temperature code with us, without which this tutorial wouldn't be possible.

So, let's begin:

One of the most important factors in a successful aerobrake/aerocapture maneuver with an XR2 is the periapsis altitude of the trajectory. Especially when you are approaching a planet with a high velocity. Too low and you'll burn up; too high and you won't get captured by the atmosphere. Many rely on experience to help them select the correct altitude at which to perform the aerocapture, but even the most experienced -every once in a while- come by a situation where they don't really know what to do.

This tutorial will show you how to calculate in advance the lowest altitude that you can dive in an atmosphere, for a given hull temperature.

The Ravenstar uses the following to calculate the hull temperature:
Quote:
XR2 nose temp in Kelvin = effectiveOAT + ((1.4 * 3.1034e-10 * 0.642) * ((atmpressure / 2) * (airspeed^3)))
[Note: effectiveOAT, "Effective Outside Air Temperature", is computed from GetAtmTemperature() from the core, but of course the affect it has on hull temperature is only a factor at all where there is enough static pressure to make any difference. The effect it has varies by static pressure.
This is only for the nose hull temp, but it's the only one we need, since it's the highest temperature during an aerobrake. It is safe to assume that OAT is negligable during the initial part of the aerobrake.

The atmospheric pressure is directly linked to the altitude. For most of the planets we can find the pressure for a given altitude by:

(from Orbitersdk\doc\API_guide.pdf)

Earth, Venus and Mars however, have custom atmospheric models, so we need a table with the static pressure at a range of altitudes that correspond to typical reentries.

It is pretty easy to make one:
-Run a scenario in Orbiter.
-Pause
-Scenario Editor
-Bring in a DG and place it at the planet/altitude you want.
-Unpause and pause again (really quick, it's better to be at x0.1 time accel)
-Make a note of the STP from the Surface MFD
-Repeat the last three steps for the range of altitudes you want.

Here is a table for the static pressures of all 3 planets at a range of altitudes that correspond to typical (and some not so typical) aerobrake maneuvers:

 Planet Earth ALT(km) Pressure (Pa) 45 149.095894 46 131.335401 47 115.846202 48 102.290944 49 90.332336 50 79.774900 51 70.454025 52 62.585778 53 54.870070 54 48.334190 55 42.521857 56 37.359170 57 32.779092 58 28.720982 59 25.129928 60 21.956319 61 19.155356 62 16.686657 63 14.513831 64 12.604141 65 10.928158 66 9.459474 67 8.174416 68 7.051774 69 6.072592 70 5.219932 71 4.492472 72 3.832674 73 3.279521 74 2.800236 75 2.387590 76 2.032800 77 1.728172 78 1.466983 79 1.243359 80 1.052175 81 0.888969 82 0.749858 83 0.631467 84 0.530869 85 0.445528
 Planet Mars ALT(km) Pressure (Pa) 10 223.444645 11 201.211149 12 180.997468 13 162.637829 14 145.978606 15 130.947896 16 117.471722 17 105.389143 18 94.555333 19 84.840626 20 76.128859 21 68.292238 22 61.211232 23 54.817611 24 49.049231 25 43.849155 26 39.165244 27 34.949778 28 31.159137 29 27.753443 30 24.696293 31 21.960625 32 19.528635 33 17.367162 34 15.445985 35 13.738269 36 12.220198 37 10.870614 38 9.670737 39 8.603887 40 7.655251 41 6.811672 42 6.061465 43 5.394249 44 4.800802 45 4.272934 46 3.803365 47 3.385628 48 3.013976 49 2.683303 50 2.389071
 Planet Venus ALT(km) Pressure (Pa) 70 2,174.121143 71 1,780.922039 72 1,456.860914 73 1,189.260173 74 968.728835 75 787.360326 76 638.513600 77 516.618107 78 417.013700 79 335.806226 80 269.749596 81 216.143410 82 172.745445 83 137.697998 84 109.465603 85 86.781718 86 68.604082 87 54.076894 88 42.499266 89 33.298619 90 26.008301 91 20.248931 92 15.724136 93 12.208767 94 9.480090 95 7.361888 96 5.717444 97 4.440682 98 3.449321 99 2.679496 100 2.081652 101 1.617331 102 1.256682 103 0.976534 104 0.758901 105 0.589818 106 0.458444 107 0.356362 108 0.277032 109 0.215380 110 0.167462

Let's re-arrange the hull temp equation to find the static pressure.

The maximum nose hull temperature for the XR2 is 2840°C. I don't recommend going higher than 2500°C, since any mistake near those temperatures will result in the loss of crew and ship.
So for the hull temp we can use 2500°C = 2773.15°K

All we need to know is the airspeed at periapsis, calculate the static pressure and look up the table to find the altitude.

Here we need to remember that the hull temp is calculated using the airspeed, not the orbital velocity. For Venus, this doesn't pose much of a problem, since it rotates so slowly, but for Earth, you can have a difference of up to +/- 464 m/s depending on the direction of your trajectory at periapsis. For Mars the difference can be up to +/- 240 m/s. Since the airspeed is raised to the power of 3, such an error may have a big impact in our hull temp calculation.

In Orbiter, the atmosphere rotates with the planet, so we can easily calculate the airspeed at periapsis, if we know the orbital velocity, latitude and heading at periapsis (all given by IMFD's Map program)

Airspeed(Pe) =
Where PeV = the periapsis orbital velocity, EqRot = planet's rotation velocity at the equator = 2*π*Radius/siderial day, lat = geographical latitude of periapsis, heading = heading at periapsis.

The EqRot for Earth is 2*π*6.37101e6/86164.1 = 464.58 m/s
The EqRot for Mars is 2*π*3.38992e6/88642.7 = 240.29 m/s
Venus rotates so slowly that the difference of the orbital speed and the airspeed is negligible.

So enough with the theory, let's try an example. We'll use the scenario from jroly posted here.

-------------------------------------------------------------------------------------------
Quote:
I am coming in at a high DV of 12 to mars, is it possible to aerocapture in the XR2? tried a few times and I always burn up. Is it impossible to do?
Not at all. All you have to do is select the correct periapsis altitude so that you don't burn up and when you reach that altitude keep the vertical acceleration close to zero, until you have shed enough of your initial velocity, in order to get captured. You will need to perform an inverted aerobrake so you can use the lift of the wings to stay inside the atmosphere during the time it takes to lose the horizontal velocity.

Let's fire up the scenario in Orbiter and open IMFD's map program:

Ok, we are less than 1/2 hour from periapsis, the periapsis alt is 12.74 km below the surface (we'll fix that) and the PeV is 12.58 km/s. From the heading, we can also see that we will be arriving in a retrograde direction (274.89°) and that the periapsis geo lat is going to be 46.869°N. Let's plug everything into the airspeed equation:

Airspeed = sqrt(PeV^2 + (EqRot*cos(lat))^2 - 2*PeV*(EqRot*cos(lat))*cos(90-heading)) =
sqrt(12580^2 + (240.29*cos(46.869))^2 - 2*12580*(240.29*cos(46.869))*cos(90-274.89)) = 12743.69 m/s

Now let's plug the airspeed in the static pressure equation:

STP = (2773.15 / (1.39466796e-10*airspeed^3)) = (2773.15 / (1.39466796e-10*12743.69^3)) = 9.607645 Pa

Looking up the table we can see that for Mars, that static pressure corresponds to an altitude of slightly more than 38km.
So our first action is to use the RCS thrusters and set the periapsis altitude at 38.5 km.
This will ensure that our peak hull temp will not be higher than 2500°C.
After the periapsis correction let's have another look at the Map program:

The parameters changed a little bit, so let's redo the calculation. The difference should be small but we'll do it anyway for practise.

Airspeed = sqrt(12570^2 + (240.29*cos(46.855))^2 - 2*12570*(240.29*cos(46.855))*cos(90-275.14)) = 12733.67 m/s
STP = (2773.15 / (1.39466796e-10*12733.67^3)) = 9.630343 Pa

So it's pretty much the same; there is no need to change our periapsis altitude.
One thing to remember here, is that we won't instantly "pop up" inside the atmosphere at that altitude, but we'll go through the upper layers first. So our peak hull temp should be slightly less than the prediction (2500°C) for that altitude.

Let's go to periapsis and check the temperature. We start inverted at ~40° AoA and watch the vertical velocity and vertical acceleration in SurfaceMFD. Our goal is to get the vertical acceleration close to zero when we reach a vertical velocity of zero at periapsis. To do that, we'll start lowering the AoA (while inverted) when the vertical velocity is about -300 m/s.

Seems like we slightly overshot the periapsis. That's ok, by calculating the periapsis altitude for a hull temp of 2500°C we can afford to make such small mistakes, by giving ourselves a couple of hundred degrees room for error. Now all we need to do is hold this altitude (and drop lower as the airspeed decreases) until we are captured.
About 10 minutes later:

Welcome to Mars orbit.
--------------------------------------------------------------------------------------------

This link will get you to a google spreadsheet that makes the hull temp calculation, so all you have to do is enter the variables from IMFD's Map program and you'll get the static pressure of the lowest altitude you can dive in for a given temperature. It's been preset to 2500°C, but you can change it if you want.
When you go to the link, select File→Create Copy so you can keep your own copy of the spreadsheet. Otherwise you won't be able to use/edit it.

One last thing to keep in mind, is that this calculation will only tell you the altutude at which you can dive inside a planet's atmosphere for a given peak hull temp. Whether you can actually perform an aerocapture at that altitude depends on other factors as well.

Have fun, happy orbiting

Last edited by dgatsoulis; 06-18-2014 at 10:16 PM. Reason: Typo, thanks Ripley!
Views 6314 Comments 2
 Thanked by:

 06-20-2014, 11:50 AM #2 SanderBuruma Orbinaut thanks for the tutorial on hull temps at different altitudes! I reckon now if we can plot the maximum altitude needed to maintain hyperbolic orbit within the atmosphere vs the temperature suffered at those altitudes you/we can know what kind of approaches are and are not viable to certain celestial bodies. Naturally this is limited by the maximum amount of lift a spacecraft (lets say the XR2) can sustain before breaking apart due to excessive wing load and maximum temperatures by aerodynamic heat flux. Fortunately wing load will not get near critical until after 50m/s Y-axis acceleration and this is enough to stay in inverted atmospheric hyperbolic orbits around celestial bodies with atmospheres.
 Thanked by:
 12-29-2017, 03:00 PM #3 cr1 Promoting vegetables in space Hope this won't count as resurrecting an old thread. I found this post super interesting, but photobucket took a dump on the pictures, so here they are again from archive.org. It might be more useful to edit the original post. Quote: Originally Posted by dgatsoulis  The atmospheric pressure is directly linked to the altitude. For most of the planets we can find the pressure for a given altitude by: (from Orbitersdk\doc\API_guide.pdf) Quote: Originally Posted by dgatsoulis  Let's fire up the scenario in Orbiter and open IMFD's map program: Ok, we are less than 1/2 hour from periapsis, the periapsis alt is 12.74 km below the surface (we'll fix that) and the PeV is 12.58 km/s. Quote: Originally Posted by dgatsoulis  After the periapsis correction let's have another look at the Map program: Quote: Originally Posted by dgatsoulis  To do that, we'll start lowering the AoA (while inverted) when the vertical velocity is about -300 m/s. Seems like we slightly overshot the periapsis. Quote: Originally Posted by dgatsoulis  About 10 minutes later: Welcome to Mars orbit.
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