Trouble calculating delta-v

Skylab · December 27, 2014

I recently learned how to calculate delta-v, but every time I try it, my numbers are way off. For example, I was trying to send a craft to land on Dres. I calculated the delta-v of each stage and added all the values together, and checked how much delta-v the mission would require, including the return to Kerbin. According to my calculations the rocket would have enough delta-v, but then I wound up running out of fuel before I could actually land. I also tried calculating the delta-v of this much simpler rocket:

The amount I got was about 1740 m/s^2, but when I flew it my maximum speed before I ran out of fuel was somewhere around 470 m/s. What am I doing wrong here? Am I missing something completely obvious? :huh:

Edited December 28, 2014 by Skylab

Kerbart · December 27, 2014

For starters, can you show us how you got the 1740 m/s²?

UmbralRaptor · December 27, 2014

Where were you launching this test rocket? If it's on the surface of Kerbin, drag can obscure things (hence the 4.4-4.7 km/s to get to orbit despite the required speed being 2.2-2.3 km/s).

As for the rocket as shown, I get:

Part Mass

Mk 16 chute 0.1

Mk 1 pod 0.8

TR-18A 0.05

FL-T400 2.25 / 0.25

LV-T45* 1.5

Total 4.7 / 2.7

Assuming you're launching from the ground, average Isp with this craft will be closer to 320 s than 370 s, but let's look at both:

320*9.82*ln(4.7/2.7) == 1742 m/s

370*9.82*ln(4.7/2.7) == 2014 m/s

The 2014 m/s is something that will only be clearly obvious if you say stick the rocket at rest well beyond Eeloo's orbit, and then fire the engines in a straight line. Otherwise, non-zero burn times will have a small effect. And from a place like the surface of Kerbin, aerodynamic and gravity drag...

*I initially thought this was an LV-T30, which has a non-trivial effect

Jason Patterson · December 27, 2014

Your delta-v calculation is the maximum change in velocity that your ship can generate from its fuel. While you're flying upward, gravity drag reduces the effect of your ship's engines (that's why we do gravity turns on launch, to reduce the component of gravity against which we are burning.) While you're in an atmosphere, atmospheric drag does the same, regardless of your direction of travel.

If you find the integral of the acceleration from aerodynamic drag with respect to time and the integral of the component of the acceleration from gravity that you are opposing with respect to time, those should make up the difference between the calculated delta-v of the rocket and your actual change in velocity. Unfortunately those calculations can really only be done with a flight path simulation.

As was said previously, if you took this vessel out into space and fired the rocket prograde or retrograde to a circular orbit, you should find that the delta-v value that you calculated very nearly matches the actual change in velocity.

SaturnV · December 27, 2014

You can use KER or MechJeb to save your time calculating ÃŽâ€V, FYI.

Then, your final orbital speed Vo = ÃŽâ€Vs + ÃŽâ€V - ÃŽâ€Ve, where:

ÃŽâ€Vs = starting speed, normally 0.

ÃŽâ€V = Total ÃŽâ€V of your vessel

ÃŽâ€Ve = gravity loss, atmosphere loss, maneuver and other loss

All ÃŽâ€V are added as vector.

- - - Updated - - -

You can use KER or MechJeb to save your time calculating ÃŽâ€V, FYI.

Then, your final orbital speed Vo = ÃŽâ€Vs + ÃŽâ€V - ÃŽâ€Ve, where:

ÃŽâ€Vs = starting speed, normally 0.

ÃŽâ€V = Total ÃŽâ€V of your vessel

ÃŽâ€Ve = gravity loss, atmosphere loss, maneuver and other loss

All ÃŽâ€V are added as vector.

Crown · December 27, 2014

When I try to calculate the delta-v by hand it differs a little from what MechJeb is calculating (compared to Tsiolkovsky). It's mostly under 100m/sec but I wonder why that is.

Pecan · December 27, 2014

When I try to calculate the delta-v by hand it differs a little from what MechJeb is calculating (compared to Tsiolkovsky). It's mostly under 100m/sec but I wonder why that is.

Show your working - like your maths teacher always told you and Kerbart said above ^^. We have no way of telling whether '100m/sec' is a large or small error but, at a guess, I'd say you're not using the correct value for 'g' (see UmbralRaptor's post)

Skylab · December 28, 2014

Sorry it took so long to reply, I've been having problems with my internet connection. The equation I've been using is the one on the KSP wiki:

$699abff01f7e7d587ecbf434866c8a75.png$

I got the value of 1740.09 m/s^2 with ln(4.7/2.7) x 320 x 9.81 m/s^2. I guess gravity and atmospheric drag should account for the behavior of the smaller rocket.

Anquietas314 · December 28, 2014

Sorry it took so long to reply, I've been having problems with my internet connection. The equation I've been using is the one on the KSP wiki:
http://wiki.kerbalspaceprogram.com/w/images/math/6/9/9/699abff01f7e7d587ecbf434866c8a75.png
I got the value of 1740.09 m/s^2 with ln(4.7/2.7) x 320 x 9.81 m/s^2. I guess gravity and atmospheric drag should account for the behavior of the smaller rocket.

The problem (for the rocket in the screenshot) is that you're not using enough decimal places; the in-game mass figure rounds to 1 decimal place. The actual wet (start) mass of your rocket is 4.74, and the dry (end) mass is 2.74, which gives 1,720.53m/s at sea level and 1,989.36m/s in vacuum. It's worth mentioning that you should use the vacuum one in general because by about 15km your ISP is already more or less that of vacuum anyway (as long as you have about 5km/s - slightly less - of vacuum delta-V reserved for your launch and enough TWR you should make it to orbit no problem )

Note that for a multi-stage rocket you need to do the delta-V calculation per stage, not for the whole rocket

Also as others have said drag in the atmosphere will significantly diminish your net speed gains

Edited December 28, 2014 by armagheddonsgw

GoSlash27 · December 28, 2014

Also for whatever reason the correct surface gravity for Kerbin is actually 9.82 m/sec^2.

But mainly what arma said above:

Your answer is only ever as accurate as the lowest resolution variable you put in it. You fed in your wet and dry mass to 2 digits, so your answer is only accurate to 2 digits.

If you feed in both of these numbers to 3 digits, then your answer will only be accurate to 3 digits.

I don't go any farther than that because I don't know if g on Kerbin is precisely 9.82 m/sec or not.

Best,

-Slashy

UmbralRaptor · December 28, 2014

I don't go any farther than that because I don't know if g on Kerbin is precisely 9.82 m/sec or not.

It's much wackier (or was when I last looked): The surface gravity is 9.81 m/sÃ‚Â² at datum, but the Isp to Ve conversion is 9.82 m/sÃ‚Â². g != g :confused:

Crown · December 28, 2014

[...]I don't go any farther than that because I don't know if g on Kerbin is precisely 9.82 m/sec or not.

It's much wackier (or was when I last looked): The surface gravity is 9.81 m/sÃ‚Â² at datum, but the Isp to Ve conversion is 9.82 m/sÃ‚Â². g != g

Tsiolkovsky's formula looks like this: $gif.download?%5CDelta%20v%20%3D%20v_%5Ctext%7Be%7D%20%5Cln%20%5Cfrac%20%7Bm_0%7D%20%7Bm_1%7D$ (as Skylab said), with $gif.download?v_\text{e}$ as the exhaust velocity of the gas.

Why 9.82 m/secÃ‚Â²??? The ISP's unit seconds is just a normalisation to a unit that American an German rocket engineers understand. You get that by taking the gas's exhaust velocity and killing the meter by dividing it by a constant. Which is the standard gravity, symbol $gif.download?g_\text{0}$ . [/rant]

Show your working[...]

Attention: I am using KSP 0.25 for the calculations but I think it doesn't matter

1 x Standard Nosecone, mass: 100kg

1 x NCS Adapter, mass: 300kg

1 x MechJeb AR202, mass: 0kg (yes, no mass)

1 x RC-001S probe body, mass: 100kg

1 x kOS module flight computer, mass: 120kg

4 x FL-400 fueltank, mass(full): 9'000kg, 2'250kg each; mass(empty): 1'000kg, 250kg each

1 x LV-T45 engine, mass: 1'500kg

The engine has a thrust of 200'000N and an ISP of 370sec in vacuum; I used 9.81 for $gif.download?g_\text{0}$ and the formula $gif.download?\Delta v = I_\text{sp} \cdot 9.81 \left[\frac{m}{sec^2} \right] \ln \left(\frac {m_0} {m_1} \right)$ .

Full mass, ( $gif.download?m_0$ ): 11'120kg

Empty mass, ( $gif.download?m_1$ ): 3'125kg

That gives me: $gif.download?\Delta v = \ln \left (\frac {11$

MechJeb gives me 11'540kg as full vessel mass and 3'120kg as empty mass, so that's correct.

edit:

Ok, using 9.81m/secÃ‚Â² as $gif.download?g_\text{0}$ gives me 4'613.03m/sec but using 9.82m/secÃ‚Â² as $gif.download?g_\text{0}$ gives me 4'617.73m/sec, which is about 4'618m/sec and what MechJeb's giving me. Disregard the question, I guess.

I don't get why KSP walks away from the scientific definition and uses 9.82 instead of 9.81 m/secÃ‚Â² :-/

Edited December 28, 2014 by Crown

GoSlash27 · December 28, 2014

I don't get why KSP walks away from the scientific definition and uses 9.82 instead of 9.81 m/secÃ‚Â² :-/

Neither do I. I suspect they *intended* the surface gravity to be 9.81 m/sec^2, but for whatever reason it ended up being 9.82 instead.

Best,

-Slashy

Pecan · December 28, 2014

...which is about 4'618m/sec and what MechJeb's giving me. Disregard the question, I guess.
I don't get why KSP walks away from the scientific definition and uses 9.82 instead of 9.81 m/secÃ‚Â² :-/

As UmbralRaptor and Slashy indicated it's just one of those 'gotcha' things - good you got it sorted :-)

Jason Patterson · December 28, 2014

Neither do I. I suspect they *intended* the surface gravity to be 9.81 m/sec^2, but for whatever reason it ended up being 9.82 instead.
Best,
-Slashy

It really doesn't matter what the surface gravity on Kerbin is, the formula has absolutely nothing to do with that. If KSP's Isp calculation really does use 9.82 instead of 9.81, it's just wrong.

Think of it this way, if we built this rocket on the surface of the Mun, would it's delta-v be any different? No, even though the surface gravity there is much lower. The delta-v calculation and the actual surface gravity of the planet are completely independent of one another - as was mentioned earlier, g is used as a conversion factor, and they apparently used the wrong value for some reason.

arkie87 · December 28, 2014

Also for whatever reason the correct surface gravity for Kerbin is actually 9.82 m/sec^2.
But mainly what arma said above:
Your answer is only ever as accurate as the lowest resolution variable you put in it. You fed in your wet and dry mass to 2 digits, so your answer is only accurate to 2 digits.
If you feed in both of these numbers to 3 digits, then your answer will only be accurate to 3 digits.
I don't go any farther than that because I don't know if g on Kerbin is precisely 9.82 m/sec or not.
Best,
-Slashy

the 9.82 figure does not come from the exact value of 1g on Kerbin. It is just a constant. In KSP, it is exactly equal to 9.82 m/s2, and does not vary with altitude, planet/body/moon etc..

Thrust by definition is:

Thrust = m_dot*v_exhaust

For some reason, engineers thought it useful to define and use specific impulse when discussing rocket performance:

v_exhaust = g0*Isp

This g0 is just a conversion factor, so it is a matter of convenience and can be rounded to exactly 9.82 (or 9.81 in real life).

Red Iron Crown · December 28, 2014

Count me in the "I don't get it" camp for g_[0 being 9.82m/s² in KSP. It adds nothing of value and only confuses those trying to calculate by hand or write calculation mods. Squad pls fix.

Kartoffelkuchen · December 29, 2014

Hi, I have a similar question, but I didn't want to start another topic. WARNING: I'm bad in maths, but I want to do some calculations like this on my own.

So, I want to calculate the Delta V for an upper stage which is in a circular 100km Orbit around Kerbin. It has:

A rockomax poodle liquid engine (vac isp = 390)

Mass is 12.5t, dry mass is 4.5t

So, I started like this:

390*12.5t/4.5t=~1083m/s

Because the Mass gets less, as more fuel is burned, I calculated the LF-Fuel consumption in vacuum by the following formula, which I taught myself, and which is working pretty well.

Thrust/ISP (VAC)*9.16489=220/390*9.16498=~5.17 LF/s

One unit LiquidFuel weighs 0.005t, to get the mass which is burned in a second I caclculated:

0.005*5.17=0.02585t/s

So, 0.02585t are burned in one second. Now I take the complete fueled weight of the whole stage and calculate

12.5-0.02585=12.47415t

Now to find out how much additional deltaV I get i made this:

390*12.47415/4.5=1081m/s

1083m/s-1081m/s=2m/s --> +2m/s every second

And to now how long I can burn:

720/5.17=~139s

139s*2m/s=278m/s

278m/s+1083m/s=1361m/s full delta V

Actually, I never achieve this in game, delta v and burn time is somewhat higher... :|

Can someone tell me what I'm doing wrong?

Anquietas314 · December 29, 2014

WARNING: I'm bad in maths, but I want to do some calculations like this on my own.

Oh boy... this'll be fun. :sticktongue:

Can someone tell me what I'm doing wrong?

Yup. You're using the wrong formula.

What you should be using: deltaV = 9.82 * I_SP * ln(start mass / end mass);

ln is "natural log", or "log to the base e". Most calculator utilities you find in operating systems have a button for that.

Also note that the equation is per stage. If you have multiple stages, use the start mass and end mass (treat future stages as full here) of each stage.

GoSlash27 · December 29, 2014

Kartoffelkutchen,

Sure thing. It's actually much easier than what you've put yourself through.

12.5/4.50= 2.78 <-- wet/dry ratio

now take the natural log of 2.78

ln(2.78)= 1.02

Now multiply that by 9.82 and your Isp

1.02*9.82*390= 3,910 m/sec. (rounded to 3 digits)

That's really all there is to it.

Best,

-Slashy

Kartoffelkuchen · December 29, 2014

Whaaaat?! Oh man, I'm sitting there the whole evening creating complicated and silly formulas, and you come along with that --.--

Thanks guys!

Anquietas314 · December 29, 2014

Whaaaat?! Oh man, I'm sitting there the whole evening creating complicated and silly formulas, and you come along with that --.--
Thanks guys!

You're welcome. Something that occurs to me based on your numbers: be sure to include the empty mass of the tanks in your "dry mass" calculation. Tanks are not massless when you've drained them (it's a bit more work to determine the dry mass ingame without mods because of how the information is displayed). Also, the equation me and slashy gave you is Tsiolkovsky's rocket equation.

Pecan · December 29, 2014

Whaaaat?! Oh man, I'm sitting there the whole evening creating complicated and silly formulas, and you come along with that --.--
Thanks guys!

Fun, isn't it!

Yes, it really comes down to the only complicated thing is the natural logarithm 'ln()' function and no-one calculates logarithms by hand any more. Even pre-computer people would use slide-rules or simply look them up in published tables :-)

(In spreadsheets like Excel and LibreOffice Calc the function is "LN()")

Dry mass is easy to find in-game career-mode because the 'i'nformation button at the bottom of the VAB/SPH gives you the vehicle mass. Check it first to get the full mass then 'tweak' the fuel out of the tanks to get the empty mass.

Edit for below: thanks for that - I read your earlier post already and still didn't think of it, doh! Mods are SO much easier.

Edited December 29, 2014 by Pecan

Anquietas314 · December 29, 2014

Dry mass is easy to find in-game career-mode because the 'i'nformation button at the bottom of the VAB/SPH gives you the vehicle mass. Check it first to get the full mass then 'tweak' the fuel out of the tanks to get the empty mass.

Don't use the in-game (stock) mass readout. OP even had an issue with it!

Crown · December 29, 2014

Kartoffelkuchen, you might find the German Wikipedia article Raketengrundgleichung quite useful since it contains a little bit different information than it's English counterpart.

It really doesn't matter what the surface gravity on Kerbin is, the formula has absolutely nothing to do with that. If KSP's Isp calculation really does use 9.82 instead of 9.81, it's just wrong.[...]

[...]Squad pls fix.

That was what bugs me in the first place.

Since I used MechJeb as a reference for the delta-v calculation I think it isn't on Sqaud's side to fix this, rather than on whoever-made-MJ's side.

Trouble calculating delta-v

Recommended Posts

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Link to comment

Share on other sites

Join the conversation