1. What is Specific Impulse Calculator?

Definition: This calculator computes the specific impulse (\( I_{sp} \)), exhaust velocity (\( v_e \)), and thrust-specific fuel consumption (TSFC) of a rocket engine based on the thrust (\( F \)) and mass flow rate (\( \dot{m} \)).

Purpose: It is used in aerospace engineering to evaluate the efficiency of rocket engines, compare different propulsion systems, and optimize fuel consumption for space missions.

2. How Does the Calculator Work?

The calculator uses the following equations:

Where:

• \( I_{sp} \): Specific impulse (s)
• \( v_e \): Exhaust velocity (m/s)
• \( TSFC \): Thrust-specific fuel consumption (kg/N·s)
• \( F \): Thrust (N)
• \( \dot{m} \): Mass flow rate (kg/s)
• \( g_0 \): Standard gravity (\( g_0 = 9.80665 \, \text{m/s}^2 \))

Unit Conversions:

• Thrust (\( F \)):
  • 1 N = 1 N
  • 1 kN = 1000 N
  • 1 lbf = 4.44822 N
• Mass Flow Rate (\( \dot{m} \)):
  • 1 kg/s = 1 kg/s
  • 1 g/s = 0.001 kg/s
  • 1 lb/s = 0.453592 kg/s
• Exhaust Velocity (\( v_e \)):
  • 1 m/s = 1 m/s
  • 1 km/s = 1000 m/s
  • 1 ft/s = 0.3048 m/s
• Thrust-Specific Fuel Consumption (\( TSFC \)):
  • 1 kg/N·s = 1 kg/N·s
  • 1 g/N·s = 0.001 kg/N·s
  • 1 lb/lbf·s = 0.00980665 kg/N·s

Steps:

• Select the input mode (custom input or predefined engine).
• If using custom input, enter the thrust (\( F \)) and mass flow rate (\( \dot{m} \)) with their respective units. If using a predefined engine, select the engine from the list and view its thrust and mass flow rate.
• Convert all inputs to base units (N for thrust, kg/s for mass flow rate).
• Calculate \( I_{sp} \), \( v_e \), and \( TSFC \) using the equations above.
• Convert the results to the selected units for display (m/s, km/s, or ft/s for \( v_e \); kg/N·s, g/N·s, or lb/lbf·s for \( TSFC \)).
• Display the results with appropriate precision (4 decimal places for \( I_{sp} \) and \( v_e \), 6 decimal places for \( TSFC \)).

3. Importance of Specific Impulse Calculation

Calculating specific impulse, exhaust velocity, and TSFC is crucial for:

• Engine Efficiency: Specific impulse measures how efficiently a rocket engine uses propellant, which is critical for optimizing fuel usage in space missions.
• Performance Comparison: Comparing different engines to select the best one for a specific mission based on thrust and fuel consumption.
• Mission Planning: Estimating the amount of propellant needed to achieve a desired velocity change, ensuring the mission can be completed within the rocket's capabilities.

4. Using the Calculator

Example: Calculate the specific impulse, exhaust velocity, and TSFC for a Kouznetsov NK-33 engine with a thrust of \( F = 169,632 \, \text{N} \) and a mass flow rate of \( \dot{m} = 52.19 \, \text{kg/s} \).

1. Select the input mode as "Predefined Engine" and choose "Kouznetsov NK-33".
2. The calculator displays the engine's thrust (\( 169,632 \, \text{N} \)) and mass flow rate (\( 52.19 \, \text{kg/s} \)).
3. Click "Calculate" to compute:
   • \( I_{sp} = \frac{F}{\dot{m} g_0} = \frac{169632}{52.19 \times 9.80665} \approx \frac{169632}{511.7291} \approx 331.5487 \, \text{s} \)
   • \( v_e = I_{sp} \cdot g_0 = 331.5487 \times 9.80665 \approx 3251.1492 \, \text{m/s} \)
   • \( TSFC = \frac{\dot{m}}{F} = \frac{52.19}{169632} \approx 0.0003077 \, \text{kg/N·s} \)

5. Frequently Asked Questions (FAQ)

Q: What is specific impulse?
A: Specific impulse (\( I_{sp} \)) is a measure of how efficiently a rocket engine uses propellant, defined as the thrust per unit of propellant weight flow rate, typically measured in seconds.

Q: How is exhaust velocity related to specific impulse?
A: Exhaust velocity (\( v_e \)) is directly related to specific impulse by the equation \( v_e = I_{sp} \cdot g_0 \), where \( g_0 \) is the standard gravity (\( 9.80665 \, \text{m/s}^2 \)).

Q: What is thrust-specific fuel consumption (TSFC)?
A: TSFC measures the mass flow rate of propellant per unit of thrust produced, typically in kg/N·s, indicating how much fuel is consumed to produce a given amount of thrust.

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