Delta V Calculator: Launch in an Atmosphere & Orbit Dimensions

[Rocketguy]

So I am making a Delta V calculator. Here it is: https://www.desmos.com/calculator/hib7psndtb
Anyone know how to figure out a rocket's Delta V if it launches from in an atmosphere?
Also, if I messed up on anything (in the Delta V calculator or isp calculator), please let me know so I could fix it! Thank you!
(but the main concern is figuring out Delta V in an atmosphere)
P.S. does Delta V change depending on the dimensions of your orbit (eg. is there a difference between a 300by500 km Earth orbit and a 150by150 Earth orbit) would you need to change the variable "g"?

(also this is just for fun... what should I put as the prefix?)

 

[Rocketguy]

I found this for Delta V lost to drag: 1/2 * k1 * p0 * K * e^ ( -1/2 * a_net * t^2 * k2) * (a_net * t)^2
but have no idea what any of the variables mean...
Here is where I got it: https://www.reddit.com/r/KerbalAcad...ow_do_i_calculate_delta_v_losses_due_to_drag/
Does that look right? And can anyone explain what the variables mean? Thanks!
(Again, if you see a problem with my Delta V graph, tell me please! thanks!)

 

[Drakkith]

Anyone know how to figure out a rocket's Delta V if it launches from in an atmosphere?

Hmmm. Are you familiar with calculus? Delta-v is defined as $Δv=\int_{t_0}^{t_1} \frac{T(t)}{m(t)}, dt$, where $T(t)$ is the instantaneous thrust and $m(t)$ is the instantaneous mass.
I don't know for sure, but I'm guessing that you'd need to subtract the instantaneous losses from air friction, gravity, and other effects from the instantaneous thrust to get the net instantaneous force on the rocket. Something like $Δv=\int_{t_0}^{t_1} \frac{T(t)-F(t)}{m(t)}, dt$ perhaps? Of course, $F(t)$ itself is going to be fairly complicated since the forces acting on the rocket and from gravity and air will change over time and with changes in the rocket's trajectory as it travels.

P.S. does Delta V change depending on the dimensions of your orbit (eg. is there a difference between a 300by500 km Earth orbit and a 150by150 Earth orbit) would you need to change the variable "g"?

Yes, there is absolutely a difference. In general, a larger orbit requires more delta-v to reach, but I don't know the details of how to find how much delta-v you need to reach any specific orbit. Some highly eccentric orbits may require less delta-v than a more circular orbit, while others may require more.

 

[Rocketguy]

Hmmm. Are you familiar with calculus? Delta-v is defined as $Δv=\int_{t_0}^{t_1} \frac{T(t)}{m(t)}, dt$, where $T(t)$ is the instantaneous thrust and $m(t)$ is the instantaneous mass.
I don't know for sure, but I'm guessing that you'd need to subtract the instantaneous losses from air friction, gravity, and other effects from the instantaneous thrust to get the net instantaneous force on the rocket. Something like $Δv=\int_{t_0}^{t_1} \frac{T(t)-F(t)}{m(t)}, dt$ perhaps? Of course, $F(t)$ itself is going to be fairly complicated since the forces acting on the rocket and from gravity and air will change over time and with changes in the rocket's trajectory as it travels.
Yes, there is absolutely a difference. In general, a larger orbit requires more delta-v to reach, but I don't know the details of how to find how much delta-v you need to reach any specific orbit. Some highly eccentric orbits may require less delta-v than a more circular orbit, while others may require more.

Ok, so I got the Delta V equation completely wrong? Because if you look here:http://www.strout.net/info/science/delta-v/ it says I got it right...
And the problem with drag is the higher you go, the thinner it is. And also it depends on time in atmosphere, trajectory, velocity, and that's changing with every rocket...
Also, what are "t1" and "t0"? Thanks!

 

[Drakkith]

I found this for Delta V lost to drag: 1/2 * k1 * p0 * K * e^ ( -1/2 * a_net * t^2 * k2) * (a_net * t)^2
but have no idea what any of the variables mean...
Here is where I got it: https://www.reddit.com/r/KerbalAcad...ow_do_i_calculate_delta_v_losses_due_to_drag/
Does that look right? And can anyone explain what the variables mean? Thanks!
(Again, if you see a problem with my Delta V graph, tell me please! thanks!)

There is an entire write-up in the comments that explains everything to do with this equation, including what the variables mean. Did you read through it all? I could try to write up an entire explanation, but it would end up being just as complicated as that write-up already is. I'd be happy to try to answer any specific questions you have though.

 

[Rocketguy]

There is an entire write-up in the comments that explains everything to do with this equation, including what the variables mean. Did you read through it all? I could try to write up an entire explanation, but it would end up being just as complicated as that write-up already is. I'd be happy to try to answer any specific questions you have though.

I will go back. I didn't see them. Thank you for pointing it out.

 

[Drakkith]

Ok, so I got the Delta V equation completely wrong?

No, your equation is just a different version that's already had the integral (the 's' shaped thing in the formula) performed and a variable change.

Also, what are "t1" and "t0"?

T0 is the initial time and t1 is the final time. I assume you haven't gone through calculus yet?

 

[Rocketguy]

No, your equation is just a different version that's already had the integral (the 's' shaped thing in the formula) performed and a variable change.
T0 is the initial time and t1 is the final time. I assume you haven't gone through calculus yet?

No, I haven't gone through calculus yet. Thank you for the help. So my graph is correct?

 

[Rocketguy]

Also, what about the change in gravity depending on altitude?

 

[Drakkith]

No, I haven't gone through calculus yet. Thank you for the help. So my graph is correct?

It looks correct to me.

Also, what about the change in gravity depending on altitude?

If you're referring to 'g' in your equation, just leave it as it is.

Note that, as far as I've read, most delta-v calculations don't include things like gravity and air resistance. Instead these things are rolled into a delta-v budget.

 

[Rocketguy]

Yeah, That's kind of what I was going for.
Like, You seeyour delta v, then you see how far that rocket can get.

 

[Drakkith]

Yeah, That's kind of what I was going for.
Like, You seeyour delta v, then you see how far that rocket can get.

Unfortunately you'd need to know the specific details of the rocket's aerodynamics, or at least some sort of approximation to it, before you can even attempt to get an estimate for the delta-v lost. And then to apply these things to generate an equation you'd need to know calculus and probably differential equations. If you don't understand the drag formula (given in your reddit link above) and you haven't been through calculus yet then I don't think you can do better than to give an educated guess at how much delta-v is required to overcome drag and gravity.

If you want to try to learn more, here's a few sources I found which may or may not help:
https://space.stackexchange.com/que...a-v-loss-due-to-gravitational-pull-from-earth
https://en.wikipedia.org/wiki/Gravity_drag
https://forum.kerbalspaceprogram.co...t-larger-rockets-lose-less-delta-v-from-drag/

 

[mfb]

I_sp is always defined based on Earth's gravity, 9.81 m/s². A slider for that value doesn't make sense.

If you want to include gravity losses and drag, things get way more complicated.

 

[Rocketguy]

Can anyone help me with the Delta-V Budget? If so... Thanks!
Here it is: https://www.desmos.com/calculator/gve2r7sfl7

 

[Rocketguy]

I_sp is always defined based on Earth's gravity, 9.81 m/s². A slider for that value doesn't make sense.

If you want to include gravity losses and drag, things get way more complicated.

Ok I think I get the Isp part...
You don't change "g" for the Delta-V capacity, you do for the Delta-V budget...?

 

[Drakkith]

Can anyone help me with the Delta-V Budget? If so... Thanks!
Here it is: https://www.desmos.com/calculator/gve2r7sfl7

The delta-v budget is different for every single space mission, even with identical launch and space vehicles since the exact maneuvers are always slightly different. And figuring out the budget requires calculating all of the delta-v required by each maneuver and lost to gravity and drag. Like I said above, you need to know more advanced math skills to figure this stuff out and it's not really something that can be taught over an online forum.

That being said, there are already pre-calculated delta-v requirements if you want to know the rough amount of delta-v required to get to various planets/moons using Hohmann transfers with engine burns at periapsis. Here's an example. If you want to be more specific and take into account other types of maneuvers then you're going to have to actually learn orbital mechanics.

Ok I think I get the Isp part...
You don't change "g" for the Delta-V capacity, you do for the Delta-V budget...?

No, you don't change 'g' at all. It's built into the units used in the formula and can't be changed unless you use non-standard units. Note that you don't have a formula where you can take into account the change in gravity on the delta-v. That would require calculus. Vector calculus most likely if I had to guess.

Here's the issue. You don't know the math required to make an accurate delta-v calculator that takes into account various losses, and because of how complicated this is we can't just throw you a couple of simple algebra formulas. So you either learn the math, or you simplify your calculator.

 

[Rocketguy]

Ok... Thanks!