A Noob's Delta V question, please help

[Jimbo78]

Hello everyone

I just bought KSP about two weeks ago and have been messing around with the delta-v calculations to try and build an effective rocket. While I understand the basics of calculating Delta-V for single stage low orbit rockets, I find I am running into a bit of a snag when calculating for multiple stages for longer interplanetary missions.

The craft I built was pretty simple and was designed as a rescue craft to bring back poor Jebediah from his mission to launch a comsat into orbit. The parts are listed below:

Reentry Stage

1 - mk16 parachute

1 - Command pod mk1

4 - LT-1 Landing Struts

Reentry Stage Propulsion

1 - TR-18A Stack Decoupler

1 - A.S.A.S Module

1 - FL-R25 RCS fuel tank

2 - FL-T400 Fuel Tanks

8 - RV-105 RCS Thruster Block

1 - LV-T30 Liquid Fuel Engine

Central Thrust Stage

1 - TR-18A Stack Decoupler

3 - FL-T400 Fuel Tanks

1 - LV-T30 Liquid Fuel Engine

4 - RV-105 RCS Thruster Block

6 - TT-Radial Decoupler

Asparagus Stage Rockets

Three stage groups of 2 for a total of 6 rockets

3 - FL-T400 Fuel Tanks

1 - LV-T30 Liquid Fuel Engine

1 - Delta Deluxe Winglet

2 - EAS-4 Strut Connectors

1 - FTX-2 External Fuel Duct

2 - Sepratron 1

So that is my build, I hope it makes sense the way I structured it.

Here is how I calculated my delta - v. I am sure I did something wrong because I end up with a value that doesn't seem like it would be enough to get off Kerban.

Total Mass = 64.99

For total dry mass I took into consideration the staging of the asparagus configuration and figured it for the point after each stage would be released, so:

Post stage 1 (total mass - dry mass of stage): 64.99 - 4.34 = 60.65

Delta V for stage 1 = (9.81 * 320) * ln(64.99/62.82) = 216.962

Post stage 2 (new mass - dry mass of stage): 60.65 - 4.34 = 56.31

Delta V for stage 2 = (9.81 * 320) * ln(60.65/56.31) = 233.078

Post stage 3: 56.31 - 4.34 = 51.97

Delta V for stage 3 = 251.781

Post central stage: 51.97 - 8.55 = 43.42

Delta V for central stage = 564.26

Total Delta V = 1266.08 ????

After a test, I was able to get into a stable orbit around 100km by time I had exhausted all but my reentry fuel, this gave me a 2 full tanks for whatever maneuvers I needed to make. So as far as I can tell, I did this calculation correctly, right?

I apologize for the really long post but it is necessary to understanding the dynamics of the game fully and I appreciate any and all assistance and advice on this calculation.

Thanks!

[CaptainKipard]

I'll let better players answer the maths question. Let me just suggest a mod called "engineer redux" to you. If you don't actually want to calculate all of this it'll give you a comprehensive readout of delta-v, mass, thrust to weight ratios, thrust (in newtons), amount of time available while thrusting at full throttle, specific impulse, cost. All of those are available for individual stages as well as total. You'll be able to judge at a glance if you can get somewhere. With it you'll even be able to quickly design rockets that don't leave any debris in orbit, without actually testing your rocket in flight.

And remember more fuel and more rockets doesn't necessarily mean significant increases in delta-v

[-RanZ-]

mechjeb or another mod will tell you everything you want to know in terms of part count, mass, and deltaV per stage. I highly recommend one of those mods as they have been incredibly helpful for me.

[Mr Shifty]

...

Total Mass = 64.99

...

Three stage groups of 2 for a total of 6 rockets

3 - FL-T400 Fuel Tanks

...

Post central stage: 51.97 - 8.55 = 43.42

...

Seems like the masses must be off somewhere. I'll venture that it's impossible to have a rocket with a payload fraction of 67% that will get into orbit. When I add up all the re-entry components, I only get 7.95 tons.

And each of those FL-T400 tanks carries 2 tons of fuel. If you have 3 per rocket and 2 rockets per asparagus stage, that's 12 tons of fuel per asparagus stage, but you're only showing a mass difference of 4.34 tons.

[tavert]

The mods make it easy but don't teach you how to do the math yourself, so there's good reason to want to figure it out by hand at least once to understand it before you go using the mods to save time.

Your mass numbers are off. For each stage, you only want to subtract the propellant mass to get your rocket-equation mass ratio. Then subtract the dry mass of the tanks, engines, decouplers, etc that you drop with the stage to get the starting mass of the next stage.

[blizzy78]

The mods make it easy but don't teach you how to do the math yourself, so there's good reason to want to figure it out by hand at least once to understand it before you go using the mods to save time.

On the other hand you could argue why one would want to do the math themselves. After all it's a game, not an algebra course. If all I need is a minimum of delta-v, some reasonable TWR, and a rocket that can hold direction if told to, then I'm rather going to go the mods route to help me out. But that's just me of course.

[-RanZ-]

If you really want to do the math more power to ya but I just mentioned it in case the OP was new and not aware of the options available.

[Mr Shifty]

Here's what I get when I add up your parts (I'm using the wiki weights; hope they match the game):

Re-entry: 1.1 tons

Re-entry propulsion: 6.85 tons, with 4 tons of that = propellant

Central stage: 8.55 tons, with 6 tons of that = propellant

Each asparagus rocket: 8.365 tons, with 6 tons of that = propellant

Total weight: 66.69 tons

So, from launch

- Starting mass: 66.69 tons

- Ending mass: 66.69-2*6 = 54.69 tons

- delta-V: 9.81*320*ln(66.69/54.69)=622.7 m/s

Drop first asparagus stage

- Starting mass: 54.69 - 2*2.365 = 49.96 tons

- Ending mass: 49.96 - 2*6 = 37.96 tons

- delta-V: 9.81*320*ln(49.96/37.96)=862.3 m/s

- total delta-V: 622.7 + 862.3 = 1484.4 m/s

Drop second asparagus stage

- Starting mass: 37.96 - 2*2.365 = 33.23 tons

- Ending mass: 33.23 - 2*6 = 21.23 tons

- delta-V: 9.81*320*ln(33.23/21.23)=1406 m/s

- total delta-V: 1484.4 + 1406 = 2890.4 m/s

Drop final asparagus stage

- Staring mass: 21.23 - 2*2.365 = 16.5 tons

- Ending mass: 16.5 - 6 = 10.5 tons

- delta-V:9.81*320*ln(16.5/10.5) = 1418 m/s

- total delta-V: 2890.4 + 1418 = 4308.4 m/s <= Launch vehicle delta-V

By now, you should be in space.

Drop center stage

- Starting mass: 10.5 - 2.55 = 7.95 tons

- Ending mass: 7.95 - 4 = 3.95 tons

- delta-V:9.81*370*ln(7.95/3.95) = 2538.8 m/s <= Note higher Isp for vacuum

- total delta-V: 4308.4 + 2538.8 = 6847.2 m/s

[capi3101]

One thing I'm noting here...which radial decoupler are you using for your asparagus? The TT-70 or the TT-38K? You don't list those with the rest of the parts, which is why I'm asking. Won't affect the delta-V calculations too much.

My numbers are coming up similar to Mr. Shifty's; any differences I have are probably me accounting for the extra delta-V you have due to RCS. Which ain't much: I come up with a delta-V of 6923.5 m/s.

[Jimbo78]

Here's what I get when I add up your parts (I'm using the wiki weights; hope they match the game):

Re-entry: 1.1 tons

Re-entry propulsion: 6.85 tons, with 4 tons of that = propellant

Central stage: 8.55 tons, with 6 tons of that = propellant

Each asparagus rocket: 8.365 tons, with 6 tons of that = propellant

Total weight: 66.69 tons

So, from launch

- Starting mass: 66.69 tons

- Ending mass: 66.69-2*6 = 54.69 tons

- delta-V: 9.81*320*ln(66.69/54.69)=622.7 m/s

Drop first asparagus stage

- Starting mass: 54.69 - 2*2.365 = 49.96 tons

- Ending mass: 49.96 - 2*6 = 37.96 tons

- delta-V: 9.81*320*ln(49.96/37.96)=862.3 m/s

- total delta-V: 622.7 + 862.3 = 1484.4 m/s

Drop second asparagus stage

- Starting mass: 37.96 - 2*2.365 = 33.23 tons

- Ending mass: 33.23 - 2*6 = 21.23 tons

- delta-V: 9.81*320*ln(33.23/21.23)=1406 m/s

- total delta-V: 1484.4 + 1406 = 2890.4 m/s

Drop final asparagus stage

- Staring mass: 21.23 - 2*2.365 = 16.5 tons

- Ending mass: 16.5 - 6 = 10.5 tons

- delta-V:9.81*320*ln(16.5/10.5) = 1418 m/s

- total delta-V: 2890.4 + 1418 = 4308.4 m/s <= Launch vehicle delta-V

By now, you should be in space.

Drop center stage

- Starting mass: 10.5 - 2.55 = 7.95 tons

- Ending mass: 7.95 - 4 = 3.95 tons

- delta-V:9.81*370*ln(7.95/3.95) = 2538.8 m/s <= Note higher Isp for vacuum

- total delta-V: 4308.4 + 2538.8 = 6847.2 m/s

Thanks a bunch everyone. I see what I was doing wrong with my calculations and have been able to adjust it accordingly. Sure I know there are mods that do all this work for you but doing it myself suits my desires to understand the complexities of the game before resorting to some one's work to do it for me. Its like taking a test by looking over the shoulder of the person actually writing the answers. I've since launched several rockets that have easily obtained orbit so my next goal is docking and then on to interplanetary travel.

I appreciate your help and advice