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hal · 10-05-2017, 12:09 PM

MrTim has the right of it gentlemen.

I went to the Wikipedia page to find what I could about Delta-V and they give an example for calculating it, which very nicely approximates what is in Transhuman Space (THS).

There, they use Exhaust Velocity x Ln(Loaded mass/empty mass). Elsewhere, I had to find the key element of how Isp is derived...

By definition, it is the Exhaust Velocity divided by Gravity. Whether you measure the Exhaust Velocity in Meters per second and divide by 9.8 meters per second per second, or you measure the velocity in feet per second and divide it by 32.174 feet per second per second, you should get the same value in seconds for Isp for that given fuel.

Consequently... (assuming I'm correct!!!)

Exhaust Velocity would equal 32.174 x 395 (for the Kerosene-Oxygen example in THS) x Ln(Loaded Mass/Empty Mass). Doing the math, I get a velocity of 651.8726292 feet per second. To convert that to Miles per second, divide by 5280, and the result becomes 0.123460725 miles per second (not too far off from .15 Miles per second!)

And this is where MrTim is right...

(32.174 * Isp)/5280 can be rewritten as Isp x 32.174/5280 (to get Miles per second instead of feet per second). Net result?

32.174/5280 = 0.006093561 per my Excel spreadsheet.

Since THS used the rule of 1/2 this total Delta-V to accelerate there, and decelerate, .003 becomes .006, which matches the value just above.

It appears that the THS formula is correct after all.

Now, to reverse Engineer what the ISP has to be to get a velocity that is .15 miles per second, and reverse the steps taken above... I get the final Isp as being 479.9097032 seconds, call it 480 rounded.

So, my initial use of the formula from THS didn't take into account the fact that it was HALF the total delta V. My initial 974.79 value using THS formula, should have been divided again by 2 due to the nature of the rules in describing Delta V for THS in the first place. 974.79/2 = 487.395. This is close enough to the 480 rounded above, probably due to rounding in the original rules formula and whether they used 32.174 for the gravity in feet per second per second, or 32.17, or even simply 32. I don't know.

But my confidence in the formula is restored. :)

10-05-2017, 12:09 PM	#22
hal Join Date: Aug 2004 Location: Buffalo, New York	Re: [Spaceships] simply fuel math... MrTim has the right of it gentlemen. I went to the Wikipedia page to find what I could about Delta-V and they give an example for calculating it, which very nicely approximates what is in Transhuman Space (THS). There, they use Exhaust Velocity x Ln(Loaded mass/empty mass). Elsewhere, I had to find the key element of how Isp is derived... By definition, it is the Exhaust Velocity divided by Gravity. Whether you measure the Exhaust Velocity in Meters per second and divide by 9.8 meters per second per second, or you measure the velocity in feet per second and divide it by 32.174 feet per second per second, you should get the same value in seconds for Isp for that given fuel. Consequently... (assuming I'm correct!!!) Exhaust Velocity would equal 32.174 x 395 (for the Kerosene-Oxygen example in THS) x Ln(Loaded Mass/Empty Mass). Doing the math, I get a velocity of 651.8726292 feet per second. To convert that to Miles per second, divide by 5280, and the result becomes 0.123460725 miles per second (not too far off from .15 Miles per second!) And this is where MrTim is right... (32.174 * Isp)/5280 can be rewritten as Isp x 32.174/5280 (to get Miles per second instead of feet per second). Net result? 32.174/5280 = 0.006093561 per my Excel spreadsheet. Since THS used the rule of 1/2 this total Delta-V to accelerate there, and decelerate, .003 becomes .006, which matches the value just above. It appears that the THS formula is correct after all. Now, to reverse Engineer what the ISP has to be to get a velocity that is .15 miles per second, and reverse the steps taken above... I get the final Isp as being 479.9097032 seconds, call it 480 rounded. So, my initial use of the formula from THS didn't take into account the fact that it was HALF the total delta V. My initial 974.79 value using THS formula, should have been divided again by 2 due to the nature of the rules in describing Delta V for THS in the first place. 974.79/2 = 487.395. This is close enough to the 480 rounded above, probably due to rounding in the original rules formula and whether they used 32.174 for the gravity in feet per second per second, or 32.17, or even simply 32. I don't know. But my confidence in the formula is restored. :)