[Leejohnston]

## Specific Impulse — Why Rocket Engines Are Rated the Way They Are

### 1. The Equation

Specific impulse:

I_sp = F ÷ (ṁg)

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### 2. What Each Symbol Means

- I_sp = specific impulse (seconds)
- F = thrust
- ṁ = mass flow rate of exhaust
- g = gravitational acceleration

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### 3. What the Equation Is Telling Us

Specific impulse measures **how efficiently a rocket uses its fuel**.

Higher I_sp means more thrust per unit of fuel.

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### 4. Where It Comes From (Intuition)

It’s like fuel economy for rockets:
- low I_sp → fuel-hungry
- high I_sp → efficient

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### 5. Worked Example

If:
- thrust = 100,000 N
- mass flow = 25 kg/s

I_sp ≈ **408 seconds**

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### 6. Real-World Applications

- Engine comparison
- Mission planning
- Rocket staging
- Spacecraft design

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### 7. Common Misconceptions

- More thrust means better engine → false
- I_sp depends on rocket size → false
- High I_sp means fast rocket → false

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### Try It Yourself

Why do ion engines have very high I_sp but low thrust?