Documentation / @interstellar-tools/equations / rocketDeltaVFromVe

Function: rocketDeltaVFromVe()

function rocketDeltaVFromVe(ve: number, m0: number, mf: number): number;

Defined in: manoeuvres/rocket-delta-v-from-ve.ts:43

Compute ideal delta-v from the Tsiolkovsky rocket equation using effective exhaust velocity.

$$\mathrm{\Delta }v=v_e\ln \left(\frac{m_0}{m_f}\right)$$

Where:

• $v_e$ is the effective exhaust velocity (m/s)
• $m_0$ is initial (wet) mass before the burn (kg)
• $m_f$ is final (dry / post-burn) mass after the burn (kg)

Units

• Inputs: ve in m/s, masses in kg.
• Output: $\mathrm{\Delta }v$ in m/s.

Notes

• This is the ideal rocket equation (no gravity/drag losses, finite burn effects, steering losses, etc.).
• Requires mf < m0 to yield a positive delta-v.
• Relationship to specific impulse: $v_e=g_0{I}_{sp}$.

Parameters

Parameter	Type	Description
ve	number	Effective exhaust velocity $v_e$ in m/s (finite, > 0).
m0	number	Initial mass $m_0$ in kg (finite, > 0).
mf	number	Final mass $m_f$ in kg (finite, > 0 and < m0).

Returns

number

Ideal delta-v $\mathrm{\Delta }v$ in m/s.

Throws

If any input is not a finite number.

Throws

If ve <= 0, m0 <= 0, mf <= 0, or mf >= m0.

Example

// Example:
// ve = 3100 m/s, m0 = 1200 kg, mf = 800 kg
const dv = rocketDeltaVFromVe(3100, 1200, 800);
// dv ≈ 3100 * ln(1200/800) ≈ 1256 m/s

See

https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation Tsiolkovsky rocket equation (background and derivation)