What Is the Chapman & Allen-Eggers Reentry Deceleration Calculator?
The Allen-Eggers / Chapman formulation calculates peak mechanical deceleration loads during planetary entry.
How Does the Chapman & Allen-Eggers Reentry Deceleration Calculator Work?
Peak deceleration occurs when the vehicle slows to 1/sqrt(e) (about 60.7%) of its initial entry velocity.
Chapman & Allen-Eggers Reentry Deceleration Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
a_{\max} = \frac{V_E^2 \sin|\gamma_E|}{2 e H}, \quad V_{\text{peak}} = \frac{V_E}{\sqrt{e}} \approx 0.6065 V_E, \quad \rho_{\text{peak}} = \frac{\beta \sin|\gamma_E|}{H}
Allen-Eggers maximum deceleration and peak load conditions for ballistic entry.
How to Use the Chapman & Allen-Eggers Reentry Deceleration Calculator
- Specify entry speed, flight path angle, scale height, and vehicle ballistic coefficient.
Step-by-Step Example Calculation
Earth LEO Ballistic Entry
Input Values:
reentryVelocityMPerS:7800
flightPathAngleDeg:-2
atmosphericScaleHeightMeters:7200
ballisticCoefficientKgPerM2:300
Worked Steps: Predicts peak deceleration ~5.45 g and velocity at peak deceleration ~4,730 m/s.
Understanding Your Result
Outputs maximum g-load, velocity at peak deceleration, and atmospheric density at peak load.
Factors That Affect the Result
- Steeper entry angle gamma dramatically increases maximum g-loads on the crew and vehicle.
When Should You Use This Calculator?
- Human spaceflight corridor safety constraints and planetary probe entry sizing.
Assumptions & Limitations
- Assumes planar ballistic trajectory with constant flight path angle and exponential atmosphere.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Foundational analytical theory used across Apollo, Stardust, and Mars Curiosity mission design.