Calculating deorbit position over earth for shuttle reentry

STS

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Hello.

I am trying to calculate the deorbit position over the surface of the earth so the shuttle can safely reach KSC or other base.

This is because SSU hasn't got the "onboard" calculations for this in OPS3 implemented yet.

I already have got some data concerning the reentry (ReA 1.282º, EI 400000ft at 4472 nm), but I am still unable to calculate the deorbit burn position. From there I will follow a path that will reach the Entry Interface, from where the OPS-304 will take on. (I understand OPS 304 is not magical, and will not take me to the runway if my ReA or vertical speed is no-go).

I am trying to calculate this through elliptic geometry but it is a real pain in the neck. I am not precisely good at maths and those calculations seem particularly complicated for me, I thought to reach the solution through calculating a transfer orbit between the orbital ellipse and a "hypothetical" ellipse or circle in which the Entry Interface Point is located.

16gwhhs.png


10gcuw5.png


I got the data for distance and altitude of EI from here: http://www.orbiterwiki.org/wiki/Intuitive_Atmospheric_Entry#Entry_Profile

And I got the ReA looking at IMFD´s map function after STS-107 deorbit and at STS-107 before EI scenarios.

2jg49qp.png


This picture makes it easy but the problem begins when ellipses get involved.

Thank you very much.
 
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STS

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Thanks for answer.

Yes, I want to calculate it by hand, because I want to avoid using (as much as possible) fictional MFD´s that don´t exist on the real shuttle.

I could use BaseSync to "debug" my calculations, but I need the algorithm that BaseSync uses to give me where to burn, or the algorithm that AutoFCS used to give me the burn position. Something to make the calculation possible by hand.

Thank you.
 

boogabooga

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Can we assume a circular starting orbit then?

Do you have Excel?
If so, do you know how to use the solver?
 

boogabooga

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See attached Excel spreadsheet.

It's straightforward for a non-rotating planet.

Starting in a circular orbit of a specified altitude, perform deorbit burn. You are then at apogee in an elliptical orbit. Flight path angle and altitude are both functions of true anomaly for a given orbit and will change as you approach entry interface.

You need to find the delta-V for the deorbit burn such that the desired flight path angle (ReA) occurs at the desired entry interface altitude (EI). This will occur at some true anomaly, which also needs to be found. I have set that up using Excel's solver.

After the solver is run, you know the true anomaly of entry interface, and you know the true anomaly of the deorbit burn is 180 degrees since it occurs at the apogee of the new orbit if the starting orbit is circular. So find the angle between deorbit burn and EI. Multiply the fraction of that angle to 360 degrees by the circumference of the planet. That is the distance from deorbit burn to EI measured over the planet's surface. Add to that the distance you want EI to occur from the landing site, and you have the distance measured on the surface that the deorbit burn must occur from the landng site.

It's trickier for the actual case of a rotating planet. I don't have time to analyze the problem right now, but I think this will change the final distance depending on for example how long it takes to get from deorbit burn to EI (which itself depends on starting altitude), your inclination, and the latitude of the landing site. For now, I've added a fudge factor. Try adding a few degrees. This may be where confirmation with BaseSync MFD may be useful.
 

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boogabooga

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Did it work?

Do you understand how to use the tool?
 

STS

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Haven´t got time to test it with orbiter yet. But I took a look at the spreadsheet and it looks good.

But about the solver, I don´t know how to use it. Can it be used with LibreOffice?

Thank you, will update when I test it in orbiter.
 

boogabooga

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I don't have LibreOffice.

Does it have a solver?
 

astrosammy

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OpenOffice has a solver for linear equations only (I guess that's not enough?).

It seems to be the same for LibreOffice (which is based on OpenOffice).
 

boogabooga

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Solver automatically finds the value in a cell or cells in order for some conditions to be met somewhere else in the spreadsheet. Essentially, it lets you work backwards.

In the spreadsheet I provided, true anomaly is in input and flight path angle is an output. That's the opposite of what you want. However, AFAIK you can't solve the equation for true anomaly. The purpose of solver is to sweep through values of true anomaly until the flight path angle is the desired value.

(Actually, the sheet I provided is a bit more complicated in that it also finds deorbit burn delta-v to get the flight path angle at the desired entry interface altitude)

Basically, you put your target values for entry interface altitude and entry angle into the brown cells. The solver will sweep through the values in cells with red text until the targets are met.

You can do the same thing by hand, but it will be time consuming.

Solver comes with Excel, but must be installed. I don't know how things work in LibreOffice.
 
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