Ballistic Coefficient β (Reentry)
Compute a reentry body's ballistic coefficient from mass, drag coefficient, and reference area — the number that sets how deep it plunges before decelerating.
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The engineering
The ballistic coefficient bundles a reentry body's mass against its drag capacity into one number. Low β means a blunt, light body that sheds velocity high in the atmosphere where the air is thin and heating is gentler; high β means a dense, slender body that carries speed deep into the dense lower atmosphere before decelerating hard. It is the single parameter that dominates a first-cut trajectory and heating estimate.
Watch the reference area convention: C_D and A must be defined against the same reference (frontal area is standard for capsules). A blunt Apollo-class capsule sits near 300–400 kg/m²; a slender warhead RV runs into the tens of thousands. If your peak-heating altitude comes out wrong, the β input is almost always where the mismatch lives — double-check whether your C_D was tabulated on frontal or planform area.
Where this math comes from
The ballistic coefficient predates spaceflight — gunners and exterior ballisticians used sectional density weighted by a drag form factor to compare artillery shells long before reentry mattered. When the ICBM and manned-capsule programs of the 1950s and 60s needed to predict how a body would slow in the atmosphere, the same grouping m/(C_D·A) fell out of the equations of motion as the natural scaling parameter.
Allen and Eggers' 1958 NACA work on blunt-body reentry made the design consequence explicit: a low ballistic coefficient throws the deceleration and heat load high into the atmosphere, saving the vehicle. Regan and Anandakrishnan's Dynamics of Atmospheric Re-Entry codified β as the governing parameter in the standard reentry-trajectory treatment this card follows.
- 1958H. J. Allen & A. J. EggersShow blunt (low-β) shapes minimize reentry heating — the physical case for the parameter.
- 1961NASA Mercury programApplies ballistic-coefficient trajectory design to the first US crewed reentries.
- 1993F. J. Regan & S. M. AnandakrishnanDynamics of Atmospheric Re-Entry fixes β = m/(C_D·A) as the governing reentry parameter.
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