Reentry G Load⚠ unverified

Understanding the Parameters

• Velocity $V$ — the $V^2$ dependence means curvature loads climb steeply with speed. A hypersonic vehicle arcing through a pull-up feels enormous centripetal acceleration even for a gentle-looking curve.

• Radius of curvature $R$ — in the denominator: a tight turn (small $R$) means a high $g$-load, a broad arc (large $R$) a gentle one. This is the same physics as a car cornering — sharper curve, harder push.

• Flight-path angle $\gamma$ — the $\sin\gamma$ factor resolves the curvature acceleration onto the relevant direction (steeper paths transfer more of the turn into the felt load). The registry labels $\gamma$ dimensionless, but it is degrees (converted internally).

• The output $n$ — a $g$-load. It complements the drag-deceleration $g$-load of Reentry Deceleration: total felt load combines the along-path deceleration and this across-path (curvature) term. During a skip or a pull-up the curvature term can dominate.

Derivation (Approaching a Proof)

Any body moving at speed $V$ along a path that curves with local radius $R$ undergoes a centripetal acceleration directed toward the centre of curvature,

$$a_c = \frac{V^2}{R},$$

the standard result from circular motion (the acceleration needed to keep turning rather than fly straight). This follows from differentiating the velocity vector: as the direction rotates at angular rate $\dot\theta = V/R$, the velocity changes at rate $V\dot\theta = V^2/R$ even at constant speed.

For an entry trajectory, the component of this curvature acceleration that registers as a structural/crew load depends on the path geometry; resolving with the flight-path angle gives $a = (V^2/R)\sin\gamma$, and dividing by $g$ expresses it in the familiar $g$-units,

$$n = \frac{V^2}{R\,g}\,\sin\gamma. \qquad\blacksquare$$

This is the maneuver/pull-up load, distinct from the drag term $a=\rho V^2/(2\beta)$ (Reentry Deceleration). In a real entry the total load is the vector sum of the drag deceleration (along the path, backward) and any curvature acceleration (toward the centre of the arc); a lifting vehicle pulling up out of a steep dive can stack the two.

Dimensional check. $$\left[\frac{V^2}{R\,g}\right] = \frac{(\text{m}/\text{s})^2}{(\text{m})(\text{m}/\text{s}^2)} = \frac{\text{m}^2/\text{s}^2}{\text{m}^2/\text{s}^2} = \text{(–)},$$ and $\sin\gamma$ is dimensionless, so $n$ is a pure $g$-load. $\checkmark$

History and Development

• Centripetal acceleration. The $V^2/R$ relation traces to Huygens and Newton's analysis of circular motion in the 17th century — the same physics that governs orbits, cornering vehicles, and looping aircraft.

• Pull-up and skip loads. In entry, curvature loads matter most during pull-ups (a lifting vehicle levelling out of a steep dive) and skip trajectories (Skip Reentry Delta V), where the path bends sharply. These impose $g$-loads separate from — and sometimes exceeding — the drag deceleration.

• Guided entry. Modern guided entry (Apollo, Orion, crewed capsules) actively modulates lift to shape the trajectory's curvature, trading between downrange control, heating, and the combined $g$-load to stay inside human tolerance.

Related Concepts: Reentry Deceleration, Reentry Velocity, Ballistic Coefficient, Skip Reentry Delta V, Lift To Drag Reentry, Newton's Second Law

Notes: Registry calculator reentry-g-load (unverified). Curvature/pull-up $g$-load $n=(V^2/R g)\sin\gamma$ — distinct from the drag deceleration of Reentry Deceleration. $R$ is the trajectory radius of curvature. $\gamma$ is degrees despite the dimensionless label. All defaults $1.0$.