Making burn calculations

[EliNaut]

I've been bouncing back and fourth between flying around in the Orion CEV and the NASSP project.
The ESAS CEV addon provides a LM and the booster to make the TLI, so i've been looking to modernize my voyage to the moon.

I can set up a good trajectory in TransX, but I have the problem of not knowing when to start the burn. Sure, I get the time of when to make the manuver, but if I stick with a simple prograde burn and start it when the clock hits zero, the engines dont have enough time to complete the trajectory. This wouldnt be a problem if the EDS wasnt so limited in attitude when docked to the CEV - RCS takes up alot of fuel, is rather low powered, and of course I get drag from the CEV. Now i'm just babbling..

ANYWAYS... What I need to do is to calculate when to start the burn. So if someone could provide a simple step by step formula, it would be much appreciated. I should be able to pass on some of the ships thrusting details if anyone needs them, or if you already have the ESAS CEV and know what i'm talking about.

Continuing what I was saying before, the drag from the CEV and the high rate of fuel consumption by the RCS stops me from using IMFD to do the burn as well, since the AB doesnt accomodate for the drag too well, and usually wastes all the fuel before I even make the burn itself :dry: (even just trying to go pro/retro.. i've been doing it manually, just coasting it with short bursts, which I dont have a problem with, but again, it takes time to do that, all the more reason why I need to schedule my TLI ) Okay.. i'll shut up now.

 

[jarmonik]

Continuing what I was saying before, the drag from the CEV and the high rate of fuel consumption by the RCS stops me from using IMFD to do the burn as well

There are some attitude control problems those might waste some RCS fuel. So far, I haven't found a solution that would work with all kind of vessels. Difficult to understand how could it waste so much fuel that it becomes a major problem.

... since the AB doesnt accomodate for the drag too well.

Drag ? what drag ? do you mean payload ?

...and usually wastes all the fuel before I even make the burn itself

I don't understand. There shouldn't be any engine or RCS activity until T-180

If you are trying to make TLI using "Realtime" mode with a low thrust engine that won't work.


-----Posted Added-----


I have done the TLI efficiently using the retro thrusters of DeltaGlider. The burn took 983 seconds to complite. I don't remember how much longer the burn can be. How much thrust you got there ?

 

[EliNaut]

Well by drag I meant the change in the center of gravity by the docked Orion at the tip of the LM.

And I know how long the burn has to last.. I need to know when to start it so my launch window isnt thrown off.

If you've flown in the NASSP project, an example would be when you program the computer for the TLI countdown for say, 20minutes, it will actually start the TLI 4 minutes earlier to accomodate for the thrust rating, in order to acurately achieve the trajectory desired by the pilot.

 

[Zatnikitelman]

If you know how long the burn is supposed to last, then just split the time in half, and begin the burn when your time to the centerpoint of the burn equals half the total burn time. So if you have a maneuver set up that takes 280 seconds, begin burning the engines when you're 140 seconds away from the "centerpoint" of the burn and continue burning for another 140 seconds.

 

[vyrago]

Hey, I've been trying the same things with the CEV. I use the CEV-0d (with the 0i 606 mesh and textures), along with the ESAS EDS and LM.

Ive recently just began to learn IMFD, and its been a long process. But heres what I do.

once my EDS/LM/CEV stack in ready:

1. switch to EDS and open IMFD. I setup an OFF-SET and OFF-AXIS intercept course. I set the Tln to 270k and the Rad to 8M. (this was taken from the Free-Return Tutorial). I engage the AB. Now, there is some swinging around with all the weight, but the burn will execute alright. Checking with a shared MFD you'll notice that your planned course will hit the moon, not enter a free return. But once you separate the LM and CEV from the EDS, that usually results in that extra delta V to put you into a nice, but rather high (im trying to get it lower on the burn somehow?) lunar free return.

2. once your in the moon's SOI, switch to the LM. the orion's RCS cant swing around all that weight. manually orient the LM Retrograde, switch back to Orion and engage the Prograde autopilot. (remember, they face eachother. also, dont try using the prograde autopilots untill your nice and close to the moon, the changing gravity field will make you unstable and waste fuel.)

3. Once your close to Pe, switch back to LM and blast off the descent motor for your LOI burn. it should use about 40 of the LM fuel. the problem is that although you've made it to lunar orbit with your LM, its still too high to land. it ends up being around 2.5 x 2.6. it should be more like 1.7 or something I think.


anyways, you can use AB to burn your stack to the moon. you just have to endure some sloppy gimballing during the burn. I'm still working on a good Tln setting for a lower lunar orbit. im fairly new to this whole interplanetary stuff, most of my orbiter time has been spent flying shuttle fleet in LEO.

 

[agentgonzo]

The latest version of TransX (on orbithangar) calculates and shows you when to start your burn.


-----Posted Added-----

If you know how long the burn is supposed to last, then just split the time in half, and begin the burn when your time to the centerpoint of the burn equals half the total burn time. So if you have a maneuver set up that takes 280 seconds, begin burning the engines when you're 140 seconds away from the "centerpoint" of the burn and continue burning for another 140 seconds.

Actually, it's not that simple. Since you're using up fuel as you go, the mass of the vessel decreases and the acceleration from full thrust at the end of the burn is more than that at the start of the burn. You therefore need to start the burn more than 140s before the 'centrepoint' in your example.

How long before is more complicated. If you take the equations of motion, you can differentiate down to jerk (the rate of change of acceleration, or third derivative of position). If you assume that jerk is constant (it's not, but you need to assume at some point), you can then use these equations to calculate when you need to star your burn to end up on the same trajectory as if you had performed an instantaneous burn that gave you all of your delta-V.

Some calculations then result in the time t_b of the burn being:

t_b = t_0 + (a_0 * T) / (2 * a_0 + j * T) - T

where t_0 is the time of the instantaneous burn
T is the total time of the burn
j is the jerk

 

[C3PO]

You could aim for ½ DV at the TIG.

Get a copy of Equation MFD, http://orbithangar.com/searchid.php?ID=1176 and enter half of the desired DV. The resulting burn time should be the time to start your engines.

 

[rocketman768]

You could aim for ½ DV at the TIG.

If t_0 is the amount of time you should burn before the injection point to reach 1/2 DV, then

t_0 = m(0)/f_r * [1 - exp(-f_r/(2F) * DV)]

where m(0) is initial mass of ship in kg, f_r is propellant flow rate in kg/s, F is the total force of the thrusters in Newtons, and DV is the desired TOTAL change in velocity in m/s.

I think this is right. Someone else should verify. You have to make the assumptions that f_r is constant and is the only source of mass loss. If it's not the only source of mass loss, you could incorporate other mass loss rates into f_r as long as it is constant. You also have to assume the total mass of the ship is always positive (no biggie). Start with:

a(t) = F/m(t)
where a(t) is acceleration and m(t) is mass of the ship. So...
a(t) = F / (m(0) - f_r*t)

And then do integration to get v(t), then solve for v(t_0) = 1/2 DV

 

[joeybigO]

The latest version of TransX (on orbithangar) calculates and shows you when to start your burn.


-----Posted Added-----




Actually, it's not that simple. Since you're using up fuel as you go, the mass of the vessel decreases and the acceleration from full thrust at the end of the burn is more than that at the start of the burn. You therefore need to start the burn more than 140s before the 'centrepoint' in your example.

How long before is more complicated. If you take the equations of motion, you can differentiate down to jerk (the rate of change of acceleration, or third derivative of position). If you assume that jerk is constant (it's not, but you need to assume at some point), you can then use these equations to calculate when you need to star your burn to end up on the same trajectory as if you had performed an instantaneous burn that gave you all of your delta-V.

Some calculations then result in the time t_b of the burn being:

t_b = t_0 + (a_0 * T) / (2 * a_0 + j * T) - T

where t_0 is the time of the instantaneous burn
T is the total time of the burn
j is the jerk

I really like the use of the jerk, I would think that you are using Cherry's mathematics, or the Tgo theory, more importantly T-t.