# Specific Impulse Calculator, Formula, Specific Impulse Calculation

## Specific Impulse Calculator:

Enter the values of thrust, F(N), mass flow rate, mdot(kg/s) and standard gravity, g(m/s2) to determine the value of Specific impulse, Isp(s).

 Enter Thrust: N Enter Mass Flow Rate: kg/s Result – Specific Impulse: s

## Specific Impulse Formula:

Specific impulse measured in seconds is a crucial metric that tells us how efficiently a rocket engine converts its propellant into thrust. A higher Isp signifies better fuel efficiency for a given amount of propellant.

Specific impulse – the time a rocket engine can theoretically generate thrust equal to its own weight (at sea level) on Earth.

Thrust generated by the engine – the force that propels the rocket forward.

Mass flow rate of propellant – the rate at which propellant is burned and ejected from the engine.

Gravitational acceleration (constant value) – the acceleration due to gravity, typically taken as 9.81 m/s2 on Earth.

Propellant is burned in the rocket engine, generating hot gases. These hot gases are expelled at high velocity through the nozzle, creating a reaction force (thrust) that propels the rocket forward according to Newton’s third law of motion.

Specific impulse (Isp) essentially compares the generated thrust (F) to the amount of propellant being burned per second (mdot) while accounting for Earth’s gravity (g).

Specific impulse, Isp(s) in seconds is calculated by dividing the thrust, F(N) in Newtons by the product of mass flow rate, mdot(kg/s) in kilograms per second and standard gravity, g(m/s2) in metres per second squared.

Specific impulse, Isp(s) = F(N) / mdot(kg/s) * g(m/s2)

Isp(s) = specific impulse in seconds, s.

F(N) = thrust in Newtons, N.

mdot(kg/s) = mass flow rate in kilograms per second, kg/s.

g(m/s2) = standard gravity in metres per second squared, m/s2 (9.81m/s2).

### Specific Impulse Calculation:

#### 1. Finding Specific Impulse (Isp)

Given:

Thrust F(N)  = 500 N

Mass Flow Rate mdot(kg/s) = 0.5 kg/s

Standard gravity, g(m/s2) =  9.81m/s2

Specific impulse, Isp(s) = F(N) / mdot(kg/s) * g(m/s2)

Isp(s) = 500 / 0.5 * 9.81

Isp(s) = 500 / 4.905

Isp(s) = 101.9s.

#### 2. Determine the Mass Flow Rate (m˙\dot{m}m˙)

Given:

Specific Impulse Isp(s) = 250 s

Thrust F(N) = 980 N

Standard gravity, g(m/s2) =  9.81m/s2

Specific impulse, Isp(s) = F(N) / mdot(kg/s) * g(m/s2)

mdot(kg/s) = F(N) / Isp(s) * g(m/s2)

mdot(kg/s) = 980 / 250 * 9.81

mdot(kg/s) = 980 / 2452.5

mdot(kg/s) = 0.4kg/s.