Sutton Core
NOZZLE THEORY LAB
SUTTON ROCKET PROPULSION ELEMENTS • 9TH ED • CH. 2–3
FLAGHSIP SIMULATOR • PHASE 1

Nozzle Theory Lab

Real-time isentropic converging-diverging nozzle analysis. Change any parameter — everything updates instantly.

IDEAL ROCKET THEORY
CONSTANT γ • 1D ISENTROPIC FLOW
CHAMBER CONDITIONS
Merlin, F-1 class — dense, moderate Isp
70.0 bar
3550 K
1.220
22.5
NOZZLE GEOMETRY
16.0
Typical: 12–20 sea level • 40–150 vacuum
Current pa = 1.013 bar
NOZZLE VISUALIZATIONParametric C-D • Mach-colored walls
OVER-EXPANDED
THROATAeINLETε = 16.0
Color = local Mach number (throat M=1 → exit). Plume reacts to pe vs pa.
Isp (VACUUM)
319.1s
Isp (SEA LEVEL)
277.6s
THRUST COEFF. CF
1.5507
c* (CHAR. VEL.)
1755.6m/s
EXIT MACH
3.68
pe / pc = 0.00636
EXIT PRESSURE
0.445 bar
Te = 1425.9 K
Flow regime: OVER-EXPANDED. When pe ≈ pa the nozzle is optimally expanded for that altitude. Under-expanded (pe > pa) wastes some performance at sea level but is ideal for vacuum. Over-expanded can cause flow separation.
PERFORMANCE CURVES (at current chamber conditions)
Specific Impulse vs Expansion Ratio
Current point at ε = 16.0 → Ispvac = 319.1s
Thrust Coefficient vs Expansion Ratio
Property Distribution — Throat (x=0) to Exit (x=1)
Mach rises rapidly in the diverging section. Pressure and temperature drop.
KEY EQUATIONS (SUTTON)
AAt=1M[2+(γ−1)M2γ+1]γ+12(γ−1)\frac{A}{A_t} = \frac{1}{M}\left[\frac{2+(\gamma-1)M^2}{\gamma+1}\right]^{\frac{\gamma+1}{2(\gamma-1)}}
Area–Mach relation (isentropic)
CF=2γ2γ−1(2γ+1)γ+1γ−1(1−(pepc)γ−1γ)+ε(pe−pa)pcC_F = \sqrt{\frac{2\gamma^2}{\gamma-1}\left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{\gamma-1}}\left(1-\left(\frac{p_e}{p_c}\right)^{\frac{\gamma-1}{\gamma}}\right)} + \varepsilon\frac{(p_e-p_a)}{p_c}
Thrust coefficient
Reference: George P. Sutton & Oscar Biblarz, Rocket Propulsion Elements, 9th Edition, Chapters 2–3. All calculations use the ideal rocket assumptions (perfect gas, isentropic 1D flow, constant γ).