Skip Reentry Delta V⚠ unverified

Understanding the Parameters

• Velocity $V$ — the speed at which the skip occurs; the required $\Delta v$ scales with it, since redirecting a faster velocity vector by the same angle demands a larger change in velocity.

• Turn angle $\gamma$ — how much the flight path is bent by the atmospheric pass. The $(1 - \cos\gamma)$ factor is small for gentle turns (a shallow skip barely changes speed) and grows toward $2V$ for a full reversal. A larger turn extracts more energy and more dramatically alters the trajectory, at the cost of higher loads during the pass. The registry labels $\gamma$ dimensionless, but it is degrees.

• The output $\Delta v$ — the effective velocity change. It quantifies the "cost" (in redirected momentum) of the skip. Physically the energy to bend the path comes from aerodynamic forces (lift and drag) during the atmospheric dip, not from propulsion — so this $\Delta v$ is a characterisation of the maneuver, not fuel that must be carried.

• Why skip. A skip lets a vehicle returning at very high speed (lunar or interplanetary return, $\gtrsim 11\,\text{km/s}$) split the entry into two or more passes, keeping peak heating and $g$-load within limits on each — and reach a landing site far downrange that a single direct entry could not.

Derivation (Approaching a Proof)

Consider the velocity vector during the skip. It enters the atmospheric pass at speed $V$ along one direction and leaves with its direction rotated by the flight-path angle $\gamma$ (idealising the speed as roughly preserved for the geometric estimate). The change in the velocity vector for a rotation by $\gamma$ has magnitude found from the law of cosines on the vector triangle (two sides $V$, included angle $\gamma$):

$$|\Delta\vec v| = \sqrt{V^2 + V^2 - 2V^2\cos\gamma} = V\sqrt{2(1-\cos\gamma)} = 2V\sin\tfrac{\gamma}{2}.$$

The registry uses the closely-related along-track component of that change,

$$\Delta v = V\,(1 - \cos\gamma), \qquad\blacksquare$$

which is the drop in the forward velocity component when the vector turns by $\gamma$ (the projection $V - V\cos\gamma$). Both forms vanish for $\gamma \to 0$ (no turn, no change) and grow with the turn angle; they are two conventions for "how much velocity was redirected." The energy for this redirection is supplied aerodynamically during the pass, which is why skip entry is a way of managing entry energy rather than spending propellant.

Dimensional check. $V\,(1-\cos\gamma)$: $V$ in m/s, $(1-\cos\gamma)$ dimensionless, so $\Delta v$ is in m/s. $\checkmark$

History and Development

• Sänger–Bredt. The skip-glide concept dates to Eugen Sänger and Irene Bredt's 1940s "Silbervogel" antipodal-bomber studies, which proposed skipping off the upper atmosphere to extend range across the globe — a visionary (if impractical at the time) idea that seeded modern boost-glide and skip-entry thinking.

• Apollo's skip capability. The Apollo command module was designed for a skip entry on lunar return: dip in to bleed energy, skip back up, then re-enter — extending downrange and easing the heating of an $11\,\text{km/s}$ return. Though the flown missions mostly used direct entries, the guidance supported skip, and it remains baseline for Orion's lunar returns to reach U.S. coastal landing zones.

• Boost-glide and skip today. Hypersonic boost-glide vehicles exploit the same physics — using lift to skip and glide for extreme range — making skip trajectories a topic of renewed interest for both entry vehicles and atmospheric maneuvering.

Related Concepts: Lift To Drag Reentry, Reentry Range, Reentry Velocity, Reentry G Load, Ballistic Coefficient, Ideal Delta-V Tsiolkovsky, Reentry Deceleration

Notes: Registry calculator skip-reentry-delta-v (unverified). $\Delta v = V(1-\cos\gamma)$ — the along-track component of turning the velocity vector by $\gamma$ (the full vector change is $2V\sin(\gamma/2)$); a characterisation of the maneuver, supplied aerodynamically, not propellant. $\gamma$ is degrees despite the dimensionless label. Skip splits a high-speed entry into milder passes and extends range. All defaults $1.0$.