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# So I have a quick question on Delta-V calcuations.

## Question

When calculating Delta-V manually the equation would be DeltaV=ln(m_start/end)xISPx9.8m/s^2

Now my question is when traveling to the moon would you change the 9.8 to calculate delta v? Im just confused as 9.8m/s^s is acceleration of gravity on earth.

Thanks, Jonda

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It's always 9.81 m/s² in this formula, as it's a conversion factor to convert specific impulse measured in seconds into specific impulse measured in m/s.

In my humble opinion it does not make any sense to measure specific impulse in seconds when talking about spaceflight, but people do it for historical reasons anyway...

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On 9/25/2018 at 2:23 PM, Jonda said:

Thank you!

The role of 9.81 is used to convert the units of mass to weight (kilograms to Newtons). You don't need it if you have thrusts and weight in pounds-force and mass in pounds.

The physical interpretation of specific impulse in seconds the amount of time a rocket must be fired to use a quantity of propellant with weight (measured at one standard gravity) equal to its thrust.

Imagine a rig: engine + dummy weight + hoses delivering fuel, total mass 100kg. The hoses are connected to a tank with 100kg of fuel+oxidizer (placed on the ground, not adding to the mass). You make the rig hover (emit 981N of thrust as weight of 100kg is 981N) and measure time until all fuel is depleted. This is your specific impulse in seconds - and obviously the longer you can get the rig to hover while maintaining the same thrust the better.

And while weight of objects changes with gravity, specific impulse of engines doesn't - so the same conversion factor is used everywhere.

The interpretation of specific impulse in m/s is much simpler: just the speed of exhaust gas. Divide it by 9.81 (or 10 if you don't want to be so precise) and you have ISp in seconds.

...also, for traditional reason, ISp is always measured in seconds, even for high values. Otherwise one would say the photon drive has almost a year of specific impulse.

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On ‎9‎/‎26‎/‎2018 at 3:47 PM, bewing said:

That's what the wiki is for. The game is on the biggish side already and can't contain an entire wiki of information too.

True enough.  I can't imagine how much chaos would ensue if Squad made KSPedia user-editable.

On ‎9‎/‎24‎/‎2018 at 10:47 PM, Jonda said:

When calculating Delta-V manually the equation would be DeltaV=ln(m_start/end)xISPx9.8m/s^2

Now my question is when traveling to the moon would you change the 9.8 to calculate delta v? Im just confused as 9.8m/s^s is acceleration of gravity on earth.

To illustrate the issue a little more thoroughly, the 9.8 m/s2 came about because it eased some difficulties with conversion between imperial and metric units (seconds being one of the few units the two systems have in common).  You are correct in that a rocket engine's design (and resultant efficiency) shouldn't change with the body it orbits.

In the original formulation, the equation for delta-V is this:

Δv = vexh * ln (mw / m0)

Where:

Δv = delta-V, naturally,
ln (mw / m0) = the natural logarithm of the wet/dry mass ratio (this part is the same in both versions), and
vexh = the engine's exhaust velocity.

I can show you how to derive that, if you like, but the point is that I find this formulation much easier to understand:  if the mass ratio is higher, then that is because either the amount of fuel is higher or the amount of payload is lower, so the rocket can do more.  That makes sense:  I know that adding fuel and lightening the payload both increase delta-V.

If the exhaust velocity is higher, then it means that the propellant has more momentum, and while that can be true for a number of different reasons (including better propellants and more efficient engines), the important part is that if the exhaust has more momentum, then the rocket does, too, so it can do more.  That should also make sense:  the basic function of a rocket is to go forwards by throwing mass out the back, and conservation of momentum means that if I throw that mass out the back faster, then I also throw the rocket forwards faster--which, functionally, is an increase in delta-V.

What often makes less sense is that more efficient engines always get their delta-V increases from a higher exhaust velocity.  It may seem odd that a Terrier has a faster exhaust than a Reliant when you put them side-by-side.  It's true, nevertheless:  the Terrier squirts out fuel at a blistering rate compared to the Reliant, but it doesn't squirt out so much at a time.  That results in high efficiency but low thrust.  To better illustrate this, consider the extreme:  the Dawn ion engine essentially works by accelerating the propellant atom by atom, but it accelerates those atoms to insane velocities when it does so.  That results in equally insane delta-V (and correspondingly low thrust).  It also explains why engines have poorer efficiency when in an atmosphere:  when they have to squirt out the exhaust against atmospheric pressure, that back pressure slows the exhaust stream from the engine, which reduces delta-V.

Edited by Zhetaan
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3 hours ago, soulsource said:

It's always 9.81 m/s² in this formula, as it's a conversion factor to convert specific impulse measured in seconds into specific impulse measured in m/s.

In my humble opinion it does not make any sense to measure specific impulse in seconds when talking about spaceflight, but people do it for historical reasons anyway...

Thank you!

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Moving to Gameplay Questions.

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It’s used for converting ISP to exhaust velocity.

What kind of baffled me is how ksp chooses to use these measurements and openly display them to the player but offer no explanation to what they mean.

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4 hours ago, Not Sure said:

What kind of baffled me is how ksp chooses to use these measurements and openly display them to the player but offer no explanation to what they mean.

That's what the wiki is for. The game is on the biggish side already and can't contain an entire wiki of information too.

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To resume all that, when you use ISP, you always use 9.8 m/s^2 no matter where you are.

Why they do that, is because we Engineers are a bit lazy sometimes, and in true, it is a simplification,  because you can measure your rocket in very different ways. Example, If a rocket weights N Tons, and has a total DV of XX, is the same to say Your propulsion is going to last N seconds and the total DV is XX.

now if you have it in seconds, is somehow easier, because with the Tons you need to do all the math. and also you may still need to know how much time you need for the maneouver.

so you say it in seconds (specified for some ship with all its conditions sets), and then you only need that.

so thats why this gives both the isp value and the trust. (you can use either in your math applying similar, but not the same equations).

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On 9/25/2018 at 3:26 AM, soulsource said:

In my humble opinion it does not make any sense to measure specific impulse in seconds when talking about spaceflight, but people do it for historical reasons anyway...

I think the reason it is traditionally measured in seconds is because it was a universal unit, the mass units used in the equation didn't matter as long as they were the same because they cancelled out. This made it easier for the Germans to work with the Americans on rocketry projects, and it stuck.

What else would it be measured in? Not in a provoking way, I'm legitimately curious.

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when I said "simplifiaction" means that they cancelled out, you can measure it in Litters of fuel too. (not sure which else besides that).

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Specific impulse is basically impulse per unit of propellant, and has different units depending if you're using mass or weight (mass * force of gravity on earth).  Using weight yields a number in seconds, using mass yields a number in N * s / kg.

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3 hours ago, Kryxal said:

using mass yields a number in N * s / kg.

Since kg has units N*s2/m, i.e. m = F/a, then N*s/kg becomes m/s.  Using mass just gives the effective exhaust gas velocity.

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On 9/29/2018 at 12:42 AM, Ultimate Steve said:

I think the reason it is traditionally measured in seconds is because it was a universal unit, the mass units used in the equation didn't matter as long as they were the same because they cancelled out. This made it easier for the Germans to work with the Americans on rocketry projects, and it stuck.

What else would it be measured in? Not in a provoking way, I'm legitimately curious.﻿

Effective exhaust velocity, measured in meters per second. NASA was/is using international units anyhow.

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7 hours ago, soulsource said:

Effective exhaust velocity, measured in meters per second. NASA was/is using international units anyhow.

Ah, right. How could I forget about something that simple?

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