I’m a bit stuck on this simple question.
So the values I’ve got:
Propellant = 100,000 kg
Structure = 10,000 kg
Payload = 5000 kg
So I worked out:
Propellant fraction is 87%
Payload fraction is 4.3%
Now I need to find
“Recall the relationship between specific impulse and exhaust velocity is given by V=gI (Where g = 9.81 and I = 450). What is the change in Velocity (V)in m/s this rocket will produce if all the propellant is consumed in one stage?”
I have tried to work this out and arrived at 1436 m\s but I don’t think I am correct.
Any advice?
Many thanks
To find the change in velocity (V) that the rocket will produce if all the propellant is consumed in one stage, you can use the rocket equation, which is given as:
ΔV = Isp * g * ln(m0/mf)
Where:
ΔV is the change in velocity
Isp is the specific impulse (exhaust velocity divided by gravitational acceleration)
g is the acceleration due to gravity (9.81 m/s^2)
ln is the natural logarithm
m0 is the initial mass (including propellant)
mf is the final mass (structure + payload)
First, let's calculate m0 (initial mass) by adding the propellant, structure, and payload masses:
m0 = Propellant + Structure + Payload = 100,000 kg + 10,000 kg + 5000 kg = 115,000 kg
Next, we need to calculate mf (final mass), which is just the structure + payload mass:
mf = Structure + Payload = 10,000 kg + 5000 kg = 15,000 kg
Now, let's substitute the values into the rocket equation:
ΔV = Isp * g * ln(m0/mf)
= 450 * 9.81 * ln(115,000 kg / 15,000 kg)
= 450 * 9.81 * ln(7.67)
Using a calculator, the natural logarithm of 7.67 is approximately 2.038. So, plugging that into the equation:
ΔV ≈ 450 * 9.81 * 2.038
≈ 8947.015 m/s
Therefore, the change in velocity (ΔV) that the rocket will produce if all the propellant is consumed in one stage is approximately 8947.015 m/s.