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∆V - What, Why, How.

Question

I have decided that after spending almost 600 hours in the game (595, should be 600 by the time I'm done tonight) it's finally time. I have never learned ∆v. All I know (and this could even be wrong, i'm really quite clueless) is that ∆v is the amount of acceleration/deceleration (although deceleration is acceleration technically) a ship or stage of a ship (or anything really) is capable of with it's current mass, fuel, fuel efficiency, and thrust. please, if I am wrong, correct me. what I would like to know is how to properly calculate the ∆v needed to make it into a specific orbit, how ∆v can be calculated for any given ship you may make, and anything else important to know about ∆v. I am by no means a noob at KSP, but also by no means an expert, to give you a feel for where I'm at in terms of ability, in career mode I have landed Kerbals on Duna and Eve, crashed a probe into Eeloo, done single ship return missions to both Minmus and Mun, I have landed a class C asteroid on Kerban using only 1 ship, and in terms of aircraft, i have flown around Kerban using a single drone without refueling, and landed back at KSC (technically I plowed into the hangar at about 450 m/s as a celebration, but i've landed that exact drone 4 other times out of 5 attempts, so I could have landed it if I wanted to). I never really bothered with ∆v because I was usually able to ignore it, and just build the ship so that it looked like it would be good enough to make the trip, then I would launch under the personal decision that regardless of the failure or success of the mission, I would revert the flight after (I called these flights my simulator flights, and I considered them to not be real, that way it was a test, to see if my ship could do what it needed to do) then after a successful simulator flight I would launch for real, and regardless of success or failure, I would not revert after the flight. using that method ∆v wasn't ever NEEDED. With the addition of certain ∆v based aspects of the game in the latest update, I decided the time had come for me to finally learn how it works, and start applying it to my space program.

Many thanks,

-Water

Edited by Dihydrogen Monoxide

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Yes, you seem to understand the deltaV concept correctly. And how to "calculate" it by the seat of your pants.

The problem is that whenever you are dealing with an atmosphere, you cannot calculate deltaV precisely. And all initial launches in KSP are done in an atmosphere. Additionally, all the deltaV calculations/maps assume Hohmann transfers at optimal transfer windows. If you ever do a burn that's not optimal, your deltaV calculations will be off. And all launches from any CB are non-optimal, for example.

But if you really decide that you want to do classic deltaV stuff, then you need to search the forum for a deltaV map. And then in the editor you select the deltaV tool and click the "Vacuum" button. This will give you all your deltaV readouts assuming vacuum level efficiency/Isp on your engines (which is what the maps assume). Then you add up the deltaVs on your deltaV map to see how much you need to get where you want to go and back again. And make sure your readout for your ship says that you have that much, plus a small margin for error.

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2 hours ago, Dihydrogen Monoxide said:

what I would like to know is how to properly calculate the ∆v needed to make it into a specific orbit,

There's an equation that can tell you how fast your ship is moving at any point in any possible orbit:

If you want to go from one known orbit to another (say, low Kerbin orbit to a Mun transfer), you can calculate the speed of each orbit at their intersection, then subtract one from the other, and that's your burn magnitude (ignoring certain fudge factors for simplicity).

2 hours ago, Dihydrogen Monoxide said:

how ∆v can be calculated for any given ship you may make,

There's another equation for that:

If you know your ship's wet mass, dry mass, and exhaust velocity (=9.81m/s/s * specific impulse), you can just plug them in and get the answer.

(For multiple stages, count the fuel that burns after the current stage as part of the dry mass.)

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I would say it's not acceleration. Acceleration is specifically a change in velocity over time(or time squared to be precise) wheras delta-v doesn't care about the time, it's just change in velocity (or potential change in velocity).

Edited by Reactordrone

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1 hour ago, Dihydrogen Monoxide said:

I have decided that after spending almost 600 hours in the game (595, should be 600 by the time I'm done tonight) it's finally time. I have never learned ∆v. All I know (and this could even be wrong, i'm really quite clueless) is that ∆v is the amount of acceleration/deceleration (although deceleration is acceleration technically) a ship or stage of a ship (or anything really) is capable of with it's current mass, fuel, fuel efficiency, and thrust. please, if I am wrong, correct me. what I would like to know is how to properly calculate the ∆v needed to make it into a specific orbit, how ∆v can be calculated for any given ship you may make, and anything else important to know about ∆v. I am by no means a noob at KSP, but also by no means an expert, to give you a feel for where I'm at in terms of ability, in career mode I have landed Kerbals on Duna and Eve, crashed a probe into Eeloo, done single ship return missions to both Minmus and Mun, I have landed a class C asteroid on Kerban using only 1 ship, and in terms of aircraft, i have flown around Kerban using a single drone without refueling, and landed back at KSC (technically I plowed into the hangar at about 450 m/s as a celebration, but i've landed that exact drone 4 other times out of 5 attempts, so I could have landed it if I wanted to). I never really bothered with ∆v because I was usually able to ignore it, and just build the ship so that it looked like it would be good enough to make the trip, then I would launch under the personal decision that regardless of the failure or success of the mission, I would revert the flight after (I called these flights my simulator flights, and I considered them to not be real, that way it was a test, to see if my ship could do what it needed to do) then after a successful simulator flight I would launch for real, and regardless of success or failure, I would not revert after the flight. using that method ∆v wasn't ever NEEDED. With the addition of certain ∆v based aspects of the game in the latest update, I decided the time had come for me to finally learn how it works, and start applying it to my space program.

Many thanks,

-Water

There's some math involved. To simplify slightly but not too much, as a body moves in orbit around another body it trades altitude (potential energy) for velocity (kinetic energy) such that total energy is conserved. There's a good bit of calculus involved in deriving the formulas, but the formulas have already been derived and it's just a bit of algebra to use them; the important two are:

Tsiolkovsky's Rocket Equation, delta-V = ve ln(Mo / Mf)

Where ve is the velocity of exhaust (which is equal to Isp times the specific gravitational acceleration 9.80665 m/s²), Mo is the initial mass of the craft, including all fuel, fuel tanks, and engines, and Mf is the final mass of the craft, including empty fuel tanks and engines.

And the orbital velocity equation, v=SQRT(mu(2/r - 1/a))

Where v is velocity, mu is the standard gravitational parmeter (Newton's gravitational constant Gc times the mass of the body being orbited), r is the radius from the gravitational center of the body at the time in question (which is the altitude plus the body's radius), and a is the semi-major axis of the orbit (which is the average of the apoapsis altitude and the periapsis altitude, plus the body's radius).  When the orbit is circular, r = a and the equation simplifies to v=SQRT(mu/r)

To use an example of both calculations, say you're in low Kerbin orbit, circular at altitude 80,000m, you want to get to the Mun (altitude 11,400,000m), your craft has a mass of 5 tons, and it's powered by a Terrier.

Your current velocity is SQRT(mu/(80,000m + 600,000m)).  (You can look up various bodies' gravitational parameters on the Wiki, but Kerbin's is 3.5316×1012.) Your orbital velocity, then, is 2278.93, which is also what the read-out on the Nav Ball should show.

Your desired orbit has a semi-major axis of ((80,000 + 11,400,000)/2 + 600,000), or 6,340,000.  In such an orbit, at periapsis your craft would have a velocity of SQRT(mu(2/(80,000+600,000) - (1/6,340,000)), or 3,135.29.  The delta-V (literally, the difference between those two velocities) is 856.36, so that is how much you need to accelerate your craft.

The Terrier has a vacuum Isp of 345 seconds (the game doesn't specify that the units are in seconds, but they are), and therefore its propellant exits with an exhaust velocity of 345 s × 9.80665 m/s² = 3,383.3 m/s.  We re-arrange Tsiolkovsky's Rocket Equation to solve for Mf, getting
Mf = Mo / (EXP(delta-V/ve)).  Thus, your rocket which originally had a 5.000 ton mass before you burned to the Mun will now have a mass of 3.882 tons; you burned 1.118 tons of fuel.

Those are the two equations and how they work.  Some people put them into spreadsheets to simplify using the calculations for mission planning.  For instance,

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Delta-V is, fundamentally, the amount by which you can affect your velocity via propulsive maneuvers.

Delta-V is only one part of the story.

Atmospheric drag. Non-ideal transfers and general Oberth Effect shenanigans. Gravity assists. Aerobraking. There's a lot more to the story behind a mission in KSP.

One of the primary things to consider is the Oberth Effect. The simplest, albeit probably least useful statement of it: "the faster you are going, the more orbital energy prograde burns give you, and the more orbital energy retrograde burns shed for you."

In practice, this means that getting a maneuver done in less time often saves delta-V... though adding extra engines on reduces your delta-V (since engines are evil hateful not-propellant mass).

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On 1/26/2019 at 3:57 PM, Dihydrogen Monoxide said:

All I know (and this could even be wrong, i'm really quite clueless) is that ∆v is the amount of acceleration/deceleration (although deceleration is acceleration technically) a ship or stage of a ship (or anything really) is capable of with it's current mass, fuel, fuel efficiency, and thrust.

Pretty much, although thrust is irrelevant.  dV is calculated from the current mass, fuel, and fuel efficiency (expressed via Isp).  The thrust doesn't matter:  if you have two ships with the same mass, same amount of fuel, and same Isp, they'll both have the same dV even if one of them has an engine with 1000x the thrust of the other.

To calculate the dV of a ship by hand (i.e. without using the built-in stock indicators), you want the Tsiolkovsky rocket equation.  As quoted above,

On 1/26/2019 at 6:21 PM, MrSystems said:

Tsiolkovsky's Rocket Equation, delta-V = ve ln(Mo / Mf)﻿

Where ve is the velocity of exhaust (which is equal to Isp times the specific gravitational acceleration 9.80665 m/s²), Mo is the initial mass of the craft, including all fuel, fuel tanks, and engines, and Mf is the final mass of the craft, including empty fuel tanks and engines.

Putting this into simple KSP terms, here's how you calculate the dV of a ship:

1. Take the total mass of the ship (i.e. its current mass, including fuel)
2. Divide by the mass of the fuel
3. Take the natural logarithm (the "ln" key on a calculator)
4. Multiply by the Isp value that KSP tells you for the engine (e.g. 345 s for a Terrier in vacuum, for instance)
5. Multiply by 9.80665 m/s2 (yes, even if you're not on Kerbin)
6. That gives you the available dV in meters per second.

Thus, for example, if you have a Terrier-powered ship that has a total mass of 5 tons, of which 2 tons is propellant (LFO), then the dV would be:  345 * 9.80665 * ln(5/3) = 1728 m/s.

As for the amount of dV you need to do a particular maneuver, that depends a lot on the specific circumstances-- for straight up orbital transfers, have a look at the vis-viva equation.  If you're lifting from a planetary surface, things get more complicated because the amount of dV needed depends on TWR and ascent profile (due to gravity losses), and if there's an atmosphere involved then it gets even worse (due to aerodynamic losses), and neither gravity losses nor aero losses are easy to express in a simple equation.

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Congratulations on being chosen as one of our Threads of the Month !

Happy landings!

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It's how much you can change your speed. So as an example, it takes 400 meters per second if you are skilled enough to return from minmus flats and to kerbin.

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One detail of the Ideal Rocket Equation not being mentioned is that it presumes an idealized, single-stage rocket with uniform engine performance and 100% fuel utilization.

For a multistage rocket, you have to stack the equation, basically. If you're doing it manually, you'd calculate the ∆v for the uppermost stage first. Then you calculate ∆v again, this time for the next stage, including the wet mass of the stage above it as part of the current stage's wet and dry mass. Then again for the next stage, including the wet mass of all the above stages as part of the wet and dry mass of the current stage. Repeat until you reach your lowest stage, then add all the individual ∆v stages together.