Jump to content

Planning your rockets: What is Delta-V?


Xannari Ferrows

Recommended Posts

Hello everyone! Today we're going to answer a question that not many people ask themselves when building rockets. What is Delta-V? What does it do? Is it important? Why should I care about it? Today we will be exploring these questions and letting you know how to plan your rockets.

 

However, I need to crush your expectations first:

This is much more complicated then simply getting a mod to calculate it for you. Mods like Mechjeb and Kerbal Engineer are 2 such examples.

Our objective here is to explore the mathematics.

 

 

  Reveal hidden contents

 

If you are here, that means you have everything you need to know.

Here's our formula:

ΔV = (Isp • 9.81m/s^2) • Ln(M1/M0)

 

See, this is one of those big, scary math equations which is actually very easy once you understand what it means. Since you are here, and therefore probably don't understand what it means, here's a quick rundown on the individual parts:

Isp is the Specific Impulse of your engine. Multiply this by 9.81 [1G] to get your exhaust velocity.

Ln is your natural log

M1 is your full mass [Mass of your rocket structure + fuel]

M0 is your dry mass [Mass of just your rocket structure without the fuel]

Still a little lost?

 

  Reveal hidden contents

 

By now you should know the individual parts and their functions.

So, let's go ahead and use some examples to help visualize the equations' overall function. Imagine a rocket with 1 ton of structural mass and 1 ton of fuel mass. The engine propelling it all has a 400 Isp.

 

ΔV = (400 • 9.81m/s^2) • Ln(2/1)

 

 

  Reveal hidden contents

Alright! First equation done, but lets take it a step further. Our rocket has 30 structural tons and 15 tons of fuel. The engine is a Nuclear Engine (800 Isp).

Clearly this should be a bit harder, right?

 

 

ΔV = (800 • 9.81m/s^2) • Ln(45/30)

 

 

Think you can solve this one by yourself? Go ahead, and the answer will be below if you can't figure it out.

 

800 x 9.81m/s^2 = 7848. Ln(1.5) = 0.40546510811

7848 x 0.40546510811 = 3182.1 m/s.mickee for finding that!

 

Delta-V across stages:

 

You may have asked this question in your head: "What about Delta-V across stages?" To which I say, I'm glad you asked! This formula is simple. Even simpler than the last.

 

 

ΔVt = ΔV1 + ΔV2

 

 

This looks different from the last, but it is deceptive. All it is is 2 rocket equations duct-taped together:

 

ΔV =Stage1(Isp • 9.81m/s^2) • Ln(M1/M0) + Stage2(Isp • 9.81m/s^2) • Ln(M1/M0)

 

Look familiar? Okay, so example time.

Think of a rocket. 32 structural tons and 12 tons of fuel. 6 tons of structural weight, 500 specific impulse engine and 3 tons of fuel used for the first stage. Decouple the first stage. 800 for the second stage with the rest of the fuel used. Think you've got it? Try it out!

 

 

Basically, at the end of the day, Delta-V is the most important thing you can account for. So obviously you want as much as possible. How do you do that? Here are a few things you can do.

1. Increase your specific impulse.

2. Carry more fuel than structural mass.

3. Stage out your rockets across multiple stages.

Increasing your Specific impulse will increase Delta-V, because the number representing Isp will grow larger, thus multiplying a larger factor by your Ln(M1/M0).

Carrying more fuel increases the M1 to M0 ratio. Higher ratios result in bigger numbers. You want the highest you can get.

Stages are important! By shaving excess mass, you increase your M1 to M0 ratio even more.

 

 

EDIT: Those questions at the beginning? Well, maybe I should give those answers instead of giving them to you to answer.

What is Delta-V? Delta-V is a meaning for "Difference in Velocity". Basically how much you can change your current velocity by. 100 m/s to 300 m/s = 200 m/s Delta-V, for example. However, making burns radial to your trajectory will use the same amount of Delta-V, but not alter your velocity. Making a radial burn changes the trajectory you are on.

What does it do? The more you have, the more you can change your velocity, and/or trajectory.

 

Is it important? Absolutely! It is one of the, if not the most important factor to account for when building a rocket, or any spaceship for that matter.

Why should I care about it? If you built all of your rockets without planning your Delta-V out, you would have no idea of it's potential. Always bring extra just in case.

So ends the guide for now.

I know some of you wont get it right away, and that's fine. Read this as many times as you need to. I'll admit, I was reviewing my work for a while. However, I hope in some small way I've been able to help you with a better understanding of the mathematics of Difference in Velocity. (DV, get it?)

Please, please tell me if I missed anything, or perhaps if I need to throw in some extra information. If you have a specific question, however, I will be more than happy to provide you with an answer whenever I can.

Have a nice day to all!

Xannari

Edited by Xannari Ferrows
Update
Link to comment
Share on other sites

  mhoram said:
As a small addition, it should be noted that as stated in http://wiki.kerbalspaceprogram.com/wiki/Specific_impulse#Conversion_factor

the conversion factor in KSP is not 9.81 m/s2, but can rather be approximated by 9.82 m/s2.

Hi.

This page seems to provide data based on the specific impulse being a constant. However, with lowest mass possible, the specific impulse reaches a peak variable of 290.2, which changes our equation. However, our end result could still be rounded to 9.82. Interesting to know, I actually didn't know this!

However, the purpose of this thread is to give you a real world approximation of your rockets' Delta-V. I will add the addition to the thread, though. Thanks for telling me!

Xannari

Link to comment
Share on other sites

  Specialist290 said:
Impressive work with how you managed to explain the topic so thoroughly in such a relatively small post. I'd say this is one for the Drawing Board :)

Thank you! It'd be an honour to be on the drawing board alongside the other impressive works found there. (Now if you have a physics-less part with fuel and all other physics-less parts, what happens when you accelerate? 0/0 it just breaks the game)

Xannari

Link to comment
Share on other sites

ÃŽâ€V = (800 • 9.81m/s^2) • Ln(45/30)

Think you can solve this one by yourself? Go ahead, and the answer will be below if you can't figure it out.

800 x 9.81m/s^2 = 7848. Log2.7182818285(1.5) = 0.40546510811

7848 x 0.40546510811 = 3812.1 m/s.

i think it should be 3182.1 m/s , Unless i'm doing something wrong. i'm guessing it was just a typo

calculated with 9.82 m/s^2 the solution should be 3185.3 m/s

Link to comment
Share on other sites

  mickee said:

i think it should be 3182.1 m/s , Unless i'm doing something wrong. i'm guessing it was just a typo

calculated with 9.82 m/s^2 the solution should be 3185.3 m/s

Oh god I should feel ashamed.

Thank you for pointing this out to me. I must have had the two bass-ackwards or something. You will be credited below for fixing my biggest mistake yet.

Or did I make an approximation? I don't know. Oh god this is embarrassing...

I mean, we could go get an ice cream if it's all the same...

Xannari

Link to comment
Share on other sites

  • 3 weeks later...

This is really useful for calculating Delta-v but your original premise hasn't been answered....What is Delta-V? What does it do? Is it important? Why should I care about it?

Could you answer these, as that would be very useful to newbies such as myself.

Link to comment
Share on other sites

  SirThawkz said:
What is Delta-V? What does it do? Is it important? Why should I care about it?

Delta-v is the amount your rocket can change its velocity. If you have 1 m/s of dv, you can accelerate from 0 m/s to 1 m/s, or 1 m/s to 0 m/s, or 200 m/s to 201 m/s...

Delta-v is important because the more your rocket has of it, the 'farther' it can go, the more planets it can visit, the bigger the moons you can land on. See this: http://mononyk.us/wherecanigo.php

Link to comment
Share on other sites

  SirThawkz said:
This is really useful for calculating Delta-v but your original premise hasn't been answered....What is Delta-V? What does it do? Is it important? Why should I care about it?

Could you answer these, as that would be very useful to newbies such as myself.

Thunderous echo pretty much hit the nail on the head. I was hoping that by the end of this you'd be able to answer the questions yourself... that's what they're there for...

Although, maybe I shouldn't put things like this in the threads... It makes confuzzled.

Xannari

Link to comment
Share on other sites

  • 8 months later...

Help please. Can't make this effing equation work. Using Rockomax 64 (initial mass = 36, final mass = 4); Mainsail (mass = 6, Isp = 285)

Number of tanks needed = x, each tank with an engine

dV = 4400

Isp = 285

Payload = 10.8

initial mass = m1 = payload + tanks + fuel + engines = 10.8 + 4x + 32x + 6x = 10.8 + 42x

final mass = m0 = payload + tanks + engines = 10.8 + 4x + 6x = 10.8 + 10x

∇∨ = ln(m1÷m0) · 9.81 · Isp

ln(m1÷m0) = ∇∨ ÷ (9.81 · Isp)

(m1÷m0) = e(∇V ÷ (Isp · 9.81))

(m1÷m0) = 4.8

m1 = 4.8 · m0

10.8 + 42x = 4.8 · (10.8 + 10x)

10.8 + 42x = 52.1 + 48x

-41.3 = 6x

x = ~ -7

So I need -7 tanks to get into the sun's orbit. Dammit.

Link to comment
Share on other sites

  CosmicCharlie said:
Help please. Can't make this effing equation work. Using Rockomax 64 (initial mass = 36, final mass = 4); Mainsail (mass = 6, Isp = 285)

Number of tanks needed = x, each tank with an engine

dV = 4400

Isp = 285

Payload = 10.8

initial mass = m1 = payload + tanks + fuel + engines = 10.8 + 4x + 32x + 6x = 10.8 + 42x

final mass = m0 = payload + tanks + engines = 10.8 + 4x + 6x = 10.8 + 10x

∇∨ = ln(m1÷m0) · 9.81 · Isp

ln(m1÷m0) = ∇∨ ÷ (9.81 · Isp)

(m1÷m0) = e(∇V ÷ (Isp · 9.81))

(m1÷m0) = 4.8

m1 = 4.8 · m0

10.8 + 42x = 4.8 · (10.8 + 10x)

10.8 + 42x = 52.1 + 48x

-41.3 = 6x

x = ~ -7

So I need -7 tanks to get into the sun's orbit. Dammit.

Figured it out.

No matter how many tanks you add, you will never have enough delta-v to get to the sun. A tank with a mainsail alone would not have enough delta-v.

Try reducing the number of mainsails per tank.

Link to comment
Share on other sites

  Thunderous Echo said:
Figured it out.

No matter how many tanks you add, you will never have enough delta-v to get to the sun. A tank with a mainsail alone would not have enough delta-v.

Try reducing the number of mainsails per tank.

This isn't actually true. However, I'm pretty sure 69086785 tanks worth of fuel, even with 1 mainsail, would not be worth it, especially since it really shouldn't work in the first place.

Edited by Xannari Ferrows
Link to comment
Share on other sites

Because of tank mass ratio, you'll never get more than g0*Isp*ln(9) dV for a single stage, since the full/empty ratio of KSP LFO tanks is 9. Even for KR-2L you're not going to exceed 8km/s. That's why empty fuel tank needs to be dropped via stages.

Link to comment
Share on other sites

  Xannari Ferrows said:
This isn't actually true.

What do you mean?

  FancyMouse said:
Because of tank mass ratio, you'll never get more than g0*Isp*ln(9) dV for a single stage, since the full/empty ratio of KSP LFO tanks is 9. Even for KR-2L you're not going to exceed 8km/s. That's why empty fuel tank needs to be dropped via stages.

Yes, that's another good solution.

Link to comment
Share on other sites

  Xannari Ferrows said:
The equivalent amount of fuel in any given amount of tanks can in theory get you unlimited Delta-V.

Actually, as the mass of fuel increases, the mass of tanks increases proportionally. Instead of approaching zero, the dry mass approaches a certain part of the wet mass, resulting in it approaching a certain real amount of delta-v, not infinite.

Link to comment
Share on other sites

  Thunderous Echo said:
Actually, as the mass of fuel increases, the mass of tanks increases proportionally. Instead of approaching zero, the dry mass approaches a certain part of the wet mass, resulting in it approaching a certain real amount of delta-v, not infinite.

Well with the tank mass yes, but not with just the fuel itself.

Link to comment
Share on other sites

Xennari,

Correction to the earlier correction:

g0 *used to be* approximated as 9.82 prior to 1.0. That has since been rectified. It is now 9.81 like it should be.

Proof:

g0test_zpskznaxwyc.jpg

Best,

-Slashy

- - - Updated - - -

  Xannari Ferrows said:
Well with the tank mass yes, but not with just the fuel itself.

Aye, but the tank mass matters as a practical concern since you can't add fuel without adding tank mass to hold it.

Since the LF&O tanks weigh 1/8 the fuel they contain, you will never be able to build a rocket with a Rwd higher than 9.

This sets an absolute maximum DV of Isp*9.81* ln(9), or approx. 21.6*Isp. And this is with an infinite number of fuel tanks.

Best,

-Slashy

Edited by GoSlash27
Link to comment
Share on other sites

  GoSlash27 said:

Since the LF&O tanks weigh 1/8 the fuel they contain, you will never be able to build a rocket with a Rwd higher than 9.

This sets an absolute maximum DV of Isp*9.81* ln(9), or approx. 21.6*Isp. And this is with an infinite number of fuel tanks.

Just to clarify so that other people don't get confused or misunderstand anything - this absolute maximum only applies to a single stage.

Link to comment
Share on other sites

  Thunderous Echo said:
Figured it out.

No matter how many tanks you add, you will never have enough delta-v to get to the sun. A tank with a mainsail alone would not have enough delta-v.

Try reducing the number of mainsails per tank.

Thanks Echo. It ws driving me bat.....

Also, I'm glad I sparked a conversation I can't follow.

Link to comment
Share on other sites

This thread is quite old. Please consider starting a new thread rather than reviving this one.

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...