# I don't know where to start with the calculations - rocket engine

Last year I stumbled upon the "How to design, build and test a rocket engine" pdf and since then I have been intrigued by making one (or at least calculating it). So I've been doing some research and looking on the internet and now I have:

1. Sutton's Rocket Propulsion elements 8th edition (2010) for most equations and
2. CEAgui, a GUI for NASA's CEA (Chemical Equilibrium with Applications) code for calculating the fuel metrics

Now, I've been trying to find the right equation sequence for calculating everything needed for making a rocket engine. The only thing I know accept these CEA calculated "measurements" below are the desired thrust(500N) and since I am using the same fuel, as in the video below, the L* of about 1 meter. I am basically trying to make a program that strongly resembles their's (timestamp: just over 18:00 minutes into the video). I have been stuck on the exit velocity as I don't know the Isp for fuel flow and because of circular referencing of the exit velocity and other units (sorry don't know the other name for it....like velocity and weight/mass..) I can't calculate anything. Should I just make an Isp assumption and work with that as they do in the "How to design, build...rocket engine" but they don't do it that way?

The CEA calculations:

FUEL C2H5OH 0.9600000 -234959.795 298.000

OXIDANT O2(L) 1.0000000 -12979.000 90.000

FUEL H2O(L) 0.0400000 -285841.390 298.000

O/F= 2.00000 %FUEL= 33.333333 R,EQ.RATIO= 1.000180 PHI,EQ.RATIO= 1.000213

CHAMBER THROAT

Pinf/P 1.0000 1.7710

P, BAR 20.000 11.293

T, K 3310.90 3013.12

RHO, KG/CU M 1.7688 0 1.0975 0

H, KJ/KG -2114.04 -2730.84

U, KJ/KG -3244.72 -3759.83

G, KJ/KG -39913.9 -37131.0

S, KJ/(KG)(K) 11.4168 11.4168

M, (1/n) 24.347 24.347

Cp, KJ/(KG)(K) 2.0830 2.0589

GAMMAs 1.1961 1.1988

SON VEL,M/SEC 1162.9 1110.7

MACH NUMBER 0.000 1.000

PERFORMANCE PARAMETERS

Ae/At 1.0000

CSTAR, M/SEC 1640.8

CF 0.6769

Ivac, M/SEC 2037.1

Isp, M/SEC 1110.7

• Isn't this the same as your other question space.stackexchange.com/q/45956/6944 but with more data? Suggest you close one of them. – Organic Marble Aug 19 at 20:59
• But I think you have a decent start here. You have all the throat conditions. Now figure out what your nozzle expansion ratio is going to be and you're pretty much there. – Organic Marble Aug 19 at 22:16

The reason you can't finish your calculations is that you are missing half of the engine. You are going to have to make some decisions about the nozzle in order to get exhaust velocity.

I'll make some decisions for you and show you how to work through it.

Your engine's design altitude is going to be 11.8 km.

This means that your nozzle exit plane pressure is going to be 0.2 bar.

(from atmosphere tables - I used the US Standard Atmosphere 1962).

You say your chamber pressure is 20 bar. Therefore the nozzle pressure ratio is 100.

Knowing this, and gamma (you say it's 1.2) we can use chart 3-5 from Sutton, 4th edition. (Subscript 1 refers to the nozzle inlet, subscript t refers to the throat) This gives you a velocity ratio of 2.5 (red arrow) and an area ratio of 11 (blue arrow).

You say the throat velocity is 1110.7 m/s.

Multiply by the velocity ratio, and you get exhaust velocity of 2776 m/s.

Don't like 11.8 km? Pick something else and redo it.

Don't like using the graph? The equations are all in Sutton. (3-25) and (3-26) in the 4th edition.

• So I've been going through the equation for the throat and exit velocity that includes R. And for those equations you should use the 8314 universal gas constant and not the 8.314. Am I just missing something here or is there something else? I went through the units and can't find what's wrong on my side. – StarshipGood Aug 20 at 14:43
• @StarshipGood Which equation? Give me a reference I can look at. – Organic Marble Aug 20 at 15:04
• Yeah sorry. The equation is 3-23 in Sutton 8th edition. For both versions of the equations, I had to use the 8314 and not 8.314. All other equation numbers from the 4th are the same in the 8th edition so it is probably the same with this one. – StarshipGood Aug 20 at 15:11
• Yeah, that is one of the many problems in the later editions. Notice it says that Vt = at. lol. The units are not even right. Here's the correct equation from the 4th edition i.imgur.com/oiWrPCS.png – Organic Marble Aug 20 at 15:16
• I saw that in the "How to design, build and test..." already and also checked here so I always divide the universal one with M. I still don't understand why they changed a totaly fine equation with a wrong one. – StarshipGood Aug 20 at 17:20