Laythe LV-N Isp

[Carsogen]

Hi there, does anyone happen to know what the specific impulse of the atomic rocket motor is at sea level on Laythe? Thanks

Cas.

Edited October 2, 2014 by Carsogen

[capi3101]

Oughta be somewhere in the neighborhood of 336, if I'm doing the math right. Laythe's sea level air pressure is 80% that of Kerbin's.

[UmbralRaptor]

Isp varies linearly with pressure (while the pressure is below 1 atm), so you can look at it as:

Isp(pressure) = Isp(vacuum) - pressure * change_in_Isp

eg: for an LV-N at sea level on Laythe: Isp = 800 - 0.8*580 = 336 (ads capi3101 got)

Pressure with respect to altitude is a bit more complicated, as it falls off exponentially:

P(altitude) = P(datum)*exp(-altitude/scale_height)

Datum pressures and scale heights are available on the wiki. Note that once you're a few scale heights above the 1 atm line, you're essentially at vacuum pressures.

[Renegrade]

Oughta be somewhere in the neighborhood of 336, if I'm doing the math right. Laythe's sea level air pressure is 80% that of Kerbin's.

My math appears to confirm that.

My handy isp table-ifier gives this table for a 220/800isp engine on Laythe:

Altitude / ATM / ISP
0m 0.80a: 336.00
1000m 0.62a: 438.64
2000m 0.49a: 518.57
3000m 0.38a: 580.82
4000m 0.29a: 629.30
5000m 0.23a: 667.06
6000m 0.18a: 696.47
7000m 0.14a: 719.37
8000m 0.11a: 737.20
9000m 0.08a: 751.09
10000m 0.07a: 761.91
11000m 0.05a: 770.34
12000m 0.04a: 776.90
13000m 0.03a: 782.01
14000m 0.02a: 785.99
15000m 0.02a: 789.09
16000m 0.01a: 791.50
17000m 0.01a: 793.38
18000m 0.01a: 794.85
19000m 0.01a: 795.99
20000m 0.01a: 796.87
21000m 0.00a: 797.57
22000m 0.00a: 798.10
23000m 0.00a: 798.52
24000m 0.00a: 798.85
25000m 0.00a: 799.10
26000m 0.00a: 799.30
27000m 0.00a: 799.46
28000m 0.00a: 799.58
29000m 0.00a: 799.67
30000m 0.00a: 799.74
31000m 0.00a: 799.80
32000m 0.00a: 799.84
33000m 0.00a: 799.88
34000m 0.00a: 799.91
35000m 0.00a: 799.93
36000m 0.00a: 799.94
37000m 0.00a: 799.96
38000m 0.00a: 799.97
39000m 0.00a: 799.97
40000m 0.00a: 799.98
41000m 0.00a: 799.98
42000m 0.00a: 799.99
43000m 0.00a: 799.99
44000m 0.00a: 799.99
45000m 0.00a: 799.99
46000m 0.00a: 800.00

[Jimbimbibble]

Based on that data it might be worth it to use LV-N only if you don't want to bring a jet. You only have to get up to 1km before it's the most efficient rocket engine.

[Red Iron Crown]

To the mathematically inclined above, at what altitude on Kerbin does an LV-N exceed 390s of Isp? Empirically I've observed it's much lower than one would expect intuitively.

[UmbralRaptor]

To the mathematically inclined above, at what altitude on Kerbin does an LV-N exceed 390s of Isp? Empirically I've observed it's much lower than one would expect intuitively.

Marginally higher than the 1717 m of aerospike parity.

390 = 800 - P*580

P = 41/58 (~0.707 atm)

altitude = -scale_height * ln(P) ~= 1734 m

For engines with somewhat interesting heights for Isp parity, compare the quad KS-25 vs KR-2L, or LV-T30 vs Poodle

Edited October 1, 2014 by UmbralRaptor

[capi3101]

Well, using the same method as earlier, there's 580 seconds difference between sea level Isp (220) and vacuum Isp (800) for an LV-N. 390 is 170 above the sea level Isp; divide 170/580 to get 0.293, subtract from 1 to get 0.707. So it should surpass 390 when the atmospheric pressure is around 71% that of sea level. The scale equation for Kerbin from the wiki is p = e^(-alt/5000), thus:

p = e^(-alt/5000) = 0.71

-alt/5000 = ln(0.71)

alt=-5000*ln(0.71) = -5000 * -3.4249 = 17,124.52 meters

Feel free to check the math, y'all.

EDIT: Okay - one of us is definitely off...

EDIT-EDIT: And it's me. On a second calculation and ignoring the earlier rounding, I get 1,733.62 meters.

Edited October 1, 2014 by capi3101

[Red Iron Crown]

Thanks, Umbral. Especially for showing your workings, adding that to my mathematical arsenal.

Edit: Wait, which of you is correct?

[UmbralRaptor]

alt=-5000*ln(0.71) = -5000 * -3.4249

The decimal point slipped; ln(0.71) is -0.34249

[capi3101]

Yeah, UmbralRaptor had it correct first; we both wound up with the same figure after rounding when I made my second attempt.

Makes me wonder at what payload mass the LV-N becomes a viable launch engine (by which I mean stick a few SRBs that can get it up to at least 1750, decouple them and let the LV-N take over from there and get the payload into orbit). It couldn't be that terribly high...

Well...let's work that out. Minimal acceptable launch TWR is around 1.2, so let's go with that. Optimal is 1.6...

TWR = T/GM, T/(TWR*G) = M

60 / (1.2 * 9.8) = 5.102 tonnes

60 / (1.6 * 9.8) = 3.827 tonnes

delta-V = ln(M/Mo) *Isp *9.8

4500 = ln(M/Mo) * 390 *9.8

M = 3.24590Mo = 5.102, Mo = 1.57183

M = 3.24590Mo = 3.827, Mo = 1.17903

Answers that - the math says it's impossible...the dry mass of an LV-N by itself is 2.25 tonnes......

Edited October 1, 2014 by capi3101

[CalculusWarrior]

Answers that - the math says it's impossible...the dry mass of an LV-N by itself is 2.25 tonnes......

Yeah, the LV-N's TWR is by far the worst in the game, making it inadvisable for landers on planets with a good deal of gravity. (Though I do remember seeing one used on a Tylo lander once...)

[Dkmdlb]

I use a few of them on my Tylo lander - It can land and return to orbit in a single stage but just barely. It starts the de-orbit burn with a TWR < 1.

[Carsogen]

Thanks everyone for your help! I have decided to use lv-n's for my jool-5 laythe lander.

Cas.

[cantab]

Answers that - the math says it's impossible...the dry mass of an LV-N by itself is 2.25 tonnes......

Your oversight is that the Isp will continue rising as the rocket climbs.

Still, I've briefly mucked around with LV-N+SRB launchers and not had much success. The low TWR of the LV-N is the killer.

Laythe's surface gravity is lower, but I suspect it's still too high for the LV-N to be ideal.

[capi3101]

Your oversight is that the Isp will continue rising as the rocket climbs.

Yeah, I still haven't figured out a good way to figure in the change in Isp over the course of a launch; might be something worth studying. I also neglected to subtract off the delta-V necessary to get the contraption up to 1700 in the first place. I don't know if those two factors combined would be sufficient to make lifting a payload - any payload - a possibility or not. I have successfully employed LV-Ns as a launch stage rocket before...twenty-five of them in concert......