Rocket Thrust vs. Altitude | Naturally Fundamental

This graph shows how a rocket engine's thrust depends on the rocket's elevation.

Click "Launch" to start the animation, then drag the white elevation slider to change the elevation, ambient pressure, and rocket thrust. For example, moving the slider up increases elevation and thrust, and decreases ambient pressure. This visualization imitates a Falcon 9 launch from Cape Canaveral.

After interacting with the graph, what are some things you notice?

Things to Notice

Air pressure drops rather quickly near sea level.
After ~30 km, the air pressure is almost negligible.
- For context, on Falcon 9 flights, main engine cutoff (MECO) occurs around 70km, while the fairings are deployed at > 100km altitude.
Thrust increases with increased elevation and decreased ambient air pressure.

The nozzle emulates SpaceX’s sea level Merlin engines by using these values for thrust calculations:

Nozzle Throat Area: 0.042 \(m^2\)
Original Exit Area: 0.9 \(m^2\)
Combustion Chamber Temp: 3625 K
Combustion Chamber Pressure: 10.8 MPa
Exhaust Gas Molar Mass: 21.9 \(kg/kmol\)
Ambient Air Pressure: See Below
Gas Constant: 8314.46 \(J / (kmol * K)\)

The following equation and constants were used to calculate ambient air pressure at a given elevation:

\( P = P_{0} \cdot (1 - \frac{g \cdot h}{ c_{p} \cdot T_{0}}) ^ \frac{c_{p} \cdot M}{R_{0}} \)

\( p_{0} = 101325 Pa \)
\( L = 0.00976 K/m \)
\( c_{p} = 1004.685 \frac{J}{kg \cdot K} \)
\( T_{0} = 288.16 K \)
\( g = 9.80665 \frac{m}{s^2} \)
\( M = 0.0289697 \frac{kg}{mol}\)
\( R_{0} = 8.31446 \frac{J}{mol \cdot K}\)

To keep calculations manageable, a few assumptions were made. These are typical for an introductory university course on rocket design:

One-dimensional flow
Uniform, axially directed exhaust velocity
Adiabatic Flow
Homogeneous exhaust gases
No boundary layer conditions
No shockwaves or discontinuities
Exhaust is at chemical equilibrium

Things to Notice

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