Eyeballing DeltaV and TWR

[ruairiau]

Being a console player, I don't have access to DeltaV or TWR stats which makes it difficult to build ships without using external tools. What I'm trying to do is come up with some rough approximations that I can do to get places. The idea is 'eyeball maths'; being able to quickly look at a ship stage and roughly know if it's up to the job.  For any newer players, here's a really basic and overly simplified explanation of the terms (but it's enough to be dangerous).

TWR - Thrust to weight ratio; it's how fast you're gonna accelerate off the launchpad. 1 or less and you're not flying. About 1.5 is 'good'. Anymore and you're wasting fuel and probably gonna blow up.

DeltaV - Think of it like the fuel needed to get to places. Use a DeltaV map to see how much DeltaV is required to get somewhere (and hopefully back!)

 

***If you think my maths is wrong or your have an easier way to eyeball, please comment below.

TWR = Multiply the total mass by 10 (for gravity) then divide by the sum of the Kn of the engines. e.g.

Mass:14t

Engine:  (1 *  LV-T45 "Swivel") 167Kn

167/140 = About 1.2 - Woot, it flies!

 

DeltaV = Multiply Isp * 10. Then multiply by ratio of fuel divided by roughly 3 (Natural Log)

DeltaV = (Isp*10) * ((ratio)/3)

Ratio of fuel = Total mass of stage divided by total mass of stage with empty fuel tanks.

Isp = look at the engine Isp and multiply by gravity (10).

So, if a rocket is 20t, and 10t without fuel, then the fuel ratio is 2. Then divide this by 3 (natural log) = 0.66. Then multiply this by the Isp of the LV-T45 "Swivel" (350 *10) 3500.

3500*0.66 is roughly 2300m/s.

 

Edited April 8, 2019 by ruairiau

[Snark]

21 hours ago, ruairiau said:

TWR = Multiply the total mass by 10 (for gravity) then divide by the sum of the Kn of the engines. e.g.

This statement is backwards-- you want to divide the thrust by the weight, not the other way around.  However,

21 hours ago, ruairiau said:

Mass:14t

Engine:  (1 *  LV-T45 "Swivel") 167Kn

167/140 = About 1.2 - Woot, it flies! 

...your working example does do it the right way 'round, so you just wrote the description backwards-- looks like you're actually doing it correctly. 

 

21 hours ago, ruairiau said:

DeltaV = Multiply Isp * 10. Then multiply by ratio of fuel divided by roughly 3 (Natural Log) 

DeltaV = (Isp*10) * ((ratio)/3)

Ratio of fuel = Total mass of stage divided by total mass of stage with empty fuel tanks.

Isp = look at the engine Isp and multiply by gravity (10).

So, if a rocket is 20t, and 10t without fuel, then the fuel ratio is 2. Then divide this by 3 (natural log) = 0.66. Then multiply this by the Isp of the LV-T45 "Swivel" (350 *10) 3500.

3500*0.66 is roughly 2300m/s.

This is not bad, actually.  The "iffiest" part is approximating ln(x) as x/3... but that's actually not too bad, just for ballpark estimating, in the range of mass ratios that are typical.

Let's take a look at how "x/3" compares with "ln(x)" for a few sample ratios:

• Ratio = 1.5.  x/3 = 0.5, ln(x) = 0.4
• Ratio = 2.0.  x/3 = 0.66, ln(x) = 0.69
• Ratio = 3.0.  x/3 = 1.0, ln(x) = 1.1

...Not bad, actually.  Certainly it's in the same general ballpark, at least over this range-- and I'd say that most rocket stages tend to be roughly in this range, so not too bad.

If the mass ratio is significantly lower than 1.5, then it'll be off by more.  For example, if your mass ratio is 1.2, then x/3 = 0.4, but ln(x) = 0.18, so that's way off.

(For a sufficiently high mass ratio it would be off, too, but in practical terms it's pretty hard to design a rocket with a ratio above 5, so I expect that won't come up often.)

[ruairiau]

Thanks for the correction. I used to play the PC version some time ago and blindly trusted mods to calculate the TWR and deltaV; so this exercise has certainly made me understand the maths a little more. I tried building some ships last night using this 'eyeball maths' and found the TWR was easy to calculate but deltaV gets complicated real fast by staging and fuel lines.