Delta V required for raising Orbital Altitude

[spartanhoplite15]

Hi,


Is there a formula that could help me calculate the delta v for change in orbital altitude. I need this for the OMS burns in the SSU. After MECO, I end up with an altitude of about 103-110 km. I would like to raise it something like 320 km. How could I calculate the Delta V for this example. Any help would be appreicated :thumbup:

Thanks!

 

[MJR]

I mean, there are plenty of variables that will determine your ApA after MECO. One of the biggest ones that I can think of is your vertical speed. I assume you are doing this manually right?

 

[spartanhoplite15]

No, they are automatic. I just have to insert the required data (dV, TiG etc...)

 

[MJR]

You haven't messed with any input data or anything of that sort?
Cause the AP in the SSU, as far as I know for the T-9 min scenario, takes the Shuttle up to around the altitude. Then you can just perform a manual OMS-1?

 

[C3PO]

Try [ame="http://www.orbithangar.com/searchid.php?ID=1176"]Equation MFD[/ame]

 

[N_Molson]

http://www.satsig.net/orbit-research/delta-v-geo-injection-calculator.htm

I'd say around 130 m/s. Which should burn roughly 2.5 tons of propellant.

 

[MJR]

You can also use Tsiolkovsky's Rocket Equation.

 

[spartanhoplite15]

Hi C3PO, I have tried Equation MFD but it is very complicated, TBH.

N_Molson the calculator really helped and I am going to test it.

MJR, I have taken a look at Tsiolkovsky rocket equation but the part about m0 and m1 I am really having trouble with them. What I mean is that how am I supposed to know the mass of the rocket after the ignition before I even do the burn? If I am wrong at this point please correct me

Thanks.

 

[blixel]

Hi,


Is there a formula that could help me calculate the delta v for change in orbital altitude. I need this for the OMS burns in the SSU. After MECO, I end up with an altitude of about 103-110 km. I would like to raise it something like 320 km. How could I calculate the Delta V for this example. Any help would be appreicated :thumbup:

Thanks!

dgatsoulis showed me how to calculate the dV to lower my altitude. I assume there must be a way to apply this equation in the other direction.

This example uses an orbit around Mercury. We know our orbital velocity is 2993 m/s. (Which can be derived from another simple equation*.)

V=2993
G=6.67259E-11 (Gravitational Constant)
M=3.301880e23 (Mercury's Mass)
R=2.440e6 (Mercury's Radius)
Sa=20000 (starting altitude = 20km)
Ta=5000 (target altitude = 5km)


dV=V-(sqrt(2*G*M*((R+(Ta)))/((R+(Sa))*(R+(Sa)+R+(Ta)))))


In this example, we need 4.58 m/s to lower our PeA from 20km to 5km. I've tested this in Orbiter 2010 and it's very accurate.

* To derive the orbital velocity with an equation:

V=sqrt(G*M/(R+(Sa)))

 

[MJR]

Hi C3PO, I have tried Equation MFD but it is very complicated, TBH.

N_Molson the calculator really helped and I am going to test it.

MJR, I have taken a look at Tsiolkovsky rocket equation but the part about m0 and m1 I am really having trouble with them. What I mean is that how am I supposed to know the mass of the rocket after the ignition before I even do the burn? If I am wrong at this point please correct me

Thanks.

Do you mean how do you figure out the mass of the rocket prior and after the burn?

 

[Kubala95]

spartanhoplite15, I invite you to read my article, ufortunately it's written in Polish, but you can use some translator:

http://www.pvsa.pl/astrodynamika/obliczenie-astrodynamiczne-t19.html

 

[spartanhoplite15]

Do you mean how do you figure out the mass of the rocket prior and after the burn?

Yes.

---------- Post added at 01:17 AM ---------- Previous post was at 01:12 AM ----------

dgatsoulis showed me how to calculate the dV to lower my altitude. I assume there must be a way to apply this equation in the other direction.

This example uses an orbit around Mercury. We know our orbital velocity is 2993 m/s. (Which can be derived from another simple equation*.)

V=2993
G=6.67259E-11
M=3.301880e23 (Mercury's Mass)
R=2.440e6 (Mercury's Radius)
Sa=20000 (starting altitude = 20km)
Ta=5000 (target altitude = 5km)


dV=V-(sqrt(2*G*M*((R+(Ta)))/((R+(Sa))*(R+(Sa)+R+(Ta)))))


In this example, we need 4.58 m/s to lower our PeA from 20km to 5km. I've tested this in Orbiter 2010 and it's very accurate.

* To derive the orbital velocity with an equation:

V=sqrt(G*M/(R+(Sa)))

Is the G value the gravity or the gravitational constant?

---------- Post added at 01:18 AM ---------- Previous post was at 01:17 AM ----------

spartanhoplite15, I invite you to read my article, ufortunately it's written in Polish, but you can use some translator:

http://www.pvsa.pl/astrodynamika/obliczenie-astrodynamiczne-t19.html

Ok, I will take a look at it.

 

[MJR]

Yes. G is the Gravitational Constant.

But about the weight, go to Scenario Editor in-game and it should tell you total mass and propellent mass. It is dynamic and changes the instant you deplete even the slightest of fuel. So by the time you reach a stable orbit you should know the difference the masses because you would just subtract the total mass at launch from the total mass at that instant.

 

[spartanhoplite15]

Thanks guys for your effort, but I think I found the answer.

It is basically a rule of thumb.

dV=Starting Altitude (nautical miles)-Target Altitude (nautical miles)*change in velocity-2.

So lets say the starting altitude is 103 km (56 nm) and target is 320 km (173 nm).

173-56=117 nm
117*2 ft/s=234 ft/s.
234 ft/s -2 =232 ft/s

So my delta V is 232 ft/s

I found the answer here:
http://www.jiskha.com/display.cgi?id=1325131153

EDIT: The part of the equation when you subtract 2 differs in your situation. If you are raising altitude, then you add 2 and if you lower altitude, then you subtract 2.

 

[C3PO]

Hi C3PO, I have tried Equation MFD but it is very complicated, TBH.

Well, it is rocket science after all. :lol:

The MFD may initially be very confusing to use, but that's because it is very versatile. You can check the calculations in the MFD and make a spreadsheet with all the values for LEO operations. In fact that's how I used to do it.

 

[Kubala95]

Thanks guys for your effort, but I think I found the answer.

It is basically a rule of thumb.

dV=Starting Altitude (nautical miles)-Target Altitude (nautical miles)*change in velocity-2.

So lets say the starting altitude is 103 km (56 nm) and target is 320 km (173 nm).

173-56=117 nm
117*2 ft/s=234 ft/s.
234 ft/s -2 =232 ft/s

So my delta V is 232 ft/s

I found the answer here:
http://www.jiskha.com/display.cgi?id=1325131153

Using this method, you will obtain only approximate value, in my article I presented how to obtain the exact value.

 

[MJR]

As Kubala said, approximate value is not that great especially when presented with a situation where fuel is used conservatively. It is like in Physics. Would you rather find average velocity using (vf-vi)/2 or would you rather find the instantaneous velocity using vf = vi + at? It is a question of accuracy and precision.

 

[Shifty]

Use the vis-viva equation:

http://en.wikipedia.org/wiki/Vis-viva_equation

v^2=GM*((2/r)-(1/a)) where GM is the gravitation parameter of Earth (398,600.4418 km^3/s^2), r is your current radial distance from the center of the Earth (6371 km plus your altitude) and a is the semi-major axis of your orbit.

For the first part of the Hohmann transfer (raising your ApA to the new alitutude)
1) Start with your current velocity
2) Calculate your new semi-major axis after raising your ApA to the new altitude.
3) Solve for velocity with the new sma. Difference between that and step 1 is delta-V for that manuever.

Now the second part (circularizing):
4) Calculate your velocity at ApA in the new elliptical orbit. (Use the same a Step 2, but your r is now at your Ap altitude.)
5) Re-run vis-viva for a circular orbit (r=a) to get velocity.
6) Difference between step 4 and step 5 is the delta-V for circularization.

Add step 3 and step 6 for the total.

 

[spartanhoplite15]

Hi Kubala,

Could you please explain the dV2 formula (at the bottom of the page) on your thread?


Thanks.

 

[MJR]

Take the square root of all of this: 2GM multiplied by the sum of R + TA divided by the sum of R + Sa multiplied by 2R + Sa + Ta. Then take you V and subtract it from that number you calculated. Honestly that is about the easiest you can put it into terms unless you are given mathematical variables.

The other simplified version is just the entire square root of this : G times M divided by the sum of R + Sa.
Your answers should be in m/s, given that the variables you are given are in km, m/s, etc.