Burn time calculator?

[Biggen]

I wanted to create a spreadsheet to calculate burn time when given (A) dV needed, (B) Engine ISP, and (C) total weight.  I thought I could do this myself but my head is spinning from doing searches here on the forum and google.  It seems some of what I found was incorrect, and the other half I'm not sure how to interpret and put into an Excel document.

Is there a calculator or spreadsheet anywhere that has this information available?

[Spricigo]

http://wiki.kerbalspaceprogram.com/wiki/Tutorial:Advanced_Rocket_Design

Calculate the total fuel needed and divide by fuel consumption rate to get burn time.

[FullMetalMachinist]

On 2/10/2017 at 11:14 AM, Biggen said:

Is there a calculator or spreadsheet anywhere that has this information available?

Not exactly a spreadsheet, but the better burn time mod has what you want, and some other stuff. 

 

On 2/10/2017 at 11:27 AM, Spricigo said:

http://wiki.kerbalspaceprogram.com/wiki/Tutorial:Advanced_Rocket_Design

Calculate the total fuel needed and divide by fuel consumption rate to get burn time.

That will give inaccurate results when the burn times are longer than a few minutes because it doesn't take into account the higher acceleration as the ship gets lighter from burning fuel. (no it won't)

Edited February 12, 2017 by FullMetalMachinist

[Spricigo]

2 minutes ago, FullMetalMachinist said:

 

28 minutes ago, Spricigo said:

http://wiki.kerbalspaceprogram.com/wiki/Tutorial:Advanced_Rocket_Design

Calculate the total fuel needed and divide by fuel consumption rate to get burn time.

That will give inaccurate results when the burn times are longer than a few minutes because it doesn't take into account the higher acceleration as the ship gets lighter from burning fuel. 

Please clarify why there will be inaccuracies. The formula don't deal with acceleration at all, so I don’t think it matter. However the fact the burns its not instant and cosine loses may have an effect in the result.

[Rhomphaia]

3 minutes ago, FullMetalMachinist said:

 

That will give inaccurate results when the burn times are longer than a few minutes because it doesn't take into account the higher acceleration as the ship gets lighter from burning fuel. 

No it won't, If you have calculated how much fuel you need to burn from your start mass and ISP (rearrange the rocket eqn) then you have already taken the increase of acceleration into account.  this is how better burn times calculates.

 

The inaccurate method is how it is done in stock, where it is calculated using the vessels TWR.

[Biggen]

Thanks guys.

I was finally able to whip up a quick spreadsheet that allows me to see burn time given my requirements.  Makes it nice to look at this while playing with ship design in VAB.

I still have to figure out how to combine ISP for more than one engine but at least I've got it working for single engine designs

Edited February 10, 2017 by Biggen

[Snark]

8 hours ago, Spricigo said:

Calculate the total fuel needed and divide by fuel consumption rate to get burn time.

^ This, if you want to do the math by hand (or in your own spreadsheet), and don't want to have a mod (such as BetterBurnTime) do it for you. 

7 hours ago, FullMetalMachinist said:

That will give inaccurate results when the burn times are longer than a few minutes because it doesn't take into account the higher acceleration as the ship gets lighter from burning fuel.

Actually, Spricigo had it right.    (This is essentially the same math that BetterBurnTime does.)  This is  exactly how one compensates for the fact that the acceleration gets faster as the ship gets lighter.  Example:

• I need to do a burn with 1000 m/s of dV
• I do the math (using the rocket equation and plugging in my Isp) and figure out that I need, say, 10 tons of fuel to do this
• My engine consumes 0.1 tons of fuel per second
• Therefore the burn will take 100 seconds.

It works because even though the acceleration won't be constant, the fuel consumption rate will be.

 

6 hours ago, Biggen said:

I still have to figure out how to combine ISP for more than one engine but at least I've got it working for single engine designs

If all of the engines have the same Isp as each other, then the Isp of all of them will be the same as the Isp of one of them.  (For example, the Isp of a Terrier is 345 seconds.  If you have a ship powered by four Terriers, its Isp is still 345 seconds.)

If you have multiple engines simultaneously firing, and they have different Isp values from each other, you combine them thus:

Isp_combined = Σ F_n /  Σ (F_n / Isp_n)
 

...where F_n is the thrust amount of the Nth engine, and Isp_n is its Isp.

In other words, add up all the thrusts of all the engines.  Then divide that by another sum, which is generated by adding up "thrust divided by Isp" for each engine.

Example:  You have a Skipper (650 kN thrust, Isp 320 sec) and two Terriers (each 60 kN thrust, Isp 345 sec).

1. Add up the thrusts, 650 + 60 + 60 = 770 kN.
2. Add up the thrust-per-Isp numbers.  (650/320) + (60/345) + (60/345) = 2.379 kN/sec
3. Divide the former by the latter.  770 kN / 2.379 kN/sec = 323.655 sec

Thus, the Isp of the combination would be 323.655 sec.  Note that it's a whole lot closer to the Isp of the Skipper than it is to that of the Terriers.  That's because the Skipper has enormously more thrust, so it consumes the large majority of the fuel.  Since most of the fuel is being funneled through the Skipper, the Skipper's Isp predominates.

 

[Biggen]

Extremely helpful as always Snark! If you have multiple engines of the same lsp and want to figure burn time then the thrust does get combined, correct?

Here is the spreadsheet I created. Would you mind taking a peak to see if I made any errors?

https://drive.google.com/file/d/0Bxtu3LnzAChjWlNaaC00Ymtqd1E/view?usp=drivesdk

[GoSlash27]

I didn't see an explanation of the method that my spreadsheet uses, so I'll outline it here...

For a single engine of a single type, input thrust in kN and Isp. (available by right-clicking the engine)This can be calculated as stated above for multiple engines and types.
Input ship's current mass in tonnes. (available from info tab in map view)
Input DV of desired burn. (from nav ball or predetermined by the user)

Equation #1: Mass at end of burn

M_start/[e^{[DV/(9.81*I_sp)]}]= M_end

Equation #2: Average mass of ship throughout burn

(M_start+M_end)/2= M_avg

Equation #3: Average acceleration

T(kN)/M_avg(tonnes)= a (m/sec²)

Equation #4: Cumulative burn time

DV/a=t_cum (sec)

Equation #5: Burn start time

Time to node (from nav ball or predetermined by the user)- t_cum/2 = t_start

Equation #6: Burn end time

Time to node (from nav ball or predetermined by the user)+ t_cum/2 = t_start

_{HTHs,
-Slashy}

 

 

Edited February 11, 2017 by GoSlash27

[FullMetalMachinist]

@Spricigo @Rhomphaia @Snark, my apologies. No body ever likes admitting that they are wrong, but I'm afraid I must. You are all correct about the way to calculate it out. I spoke up before thinking about it thoroughly (and before my morning coffee ). Thanks for politely setting me straight.