- #1

gggnano

- 43

- 3

- TL;DR Summary
- Few resources online show the exact calculations for ion thruster's power

So after reading a great paper from Utah university (or so) they include the following equation which should apply at least to some type of electric thrusters:

P(power) = T(thrust in N)*S(specific impulse in secs)*G/(2*Efficiency)

x=(1800*1000*9.8)/(2*0.3)

x = 29,000,000 watts needed to lift a human using ion thruster on earth?

1800 = force in newtons, I am using 180kg because this amount kilograms may be an adult human + an ultra light 3d printed aircraft;

1000 = Specific impulse, this one is tricky...normally they say Isp is higher but 1000 is high yet it varies from 100 to even 6000?? for ion thrusters

9.8 = not too punctual, the Gravitational constant on Earth

2*0.3 = just some constants used to measure the efficiency, apparently you can change the 0.3 number to 0.9 assuming higher efficiency.

I did some calculations according to which using chemical energy one may get the heat from say burning sugar or dodecane or ethylene etc

and assuming 30% efficiency use heat engine -> mechanical energy and the 95% to electricity but even so the thruster will fly a couple of seconds only? Actually my calculations were for 100% efficient heat engine and 100kg or less total fuel most of which is sugar or oxygen in the case of dodecane.

Another problem is that unless the specific impulse is insanely high then a lot of gas will be lost with a thrust such as 1000 N or more. For example: 1900 N=9.8*200*x so the "x" here is the mass flow rate or in the example: 0.96 kg lost per second. For 1000 Isp it's 0.19kg and just 0.019 for 10,000 Isp, so it's linear simple calculation.

So it looks like the only way to power ion craft on earth will be using Helium 3 fusion? Which is impossible at the moment, if ever.

P(power) = T(thrust in N)*S(specific impulse in secs)*G/(2*Efficiency)

x=(1800*1000*9.8)/(2*0.3)

x = 29,000,000 watts needed to lift a human using ion thruster on earth?

1800 = force in newtons, I am using 180kg because this amount kilograms may be an adult human + an ultra light 3d printed aircraft;

1000 = Specific impulse, this one is tricky...normally they say Isp is higher but 1000 is high yet it varies from 100 to even 6000?? for ion thrusters

9.8 = not too punctual, the Gravitational constant on Earth

2*0.3 = just some constants used to measure the efficiency, apparently you can change the 0.3 number to 0.9 assuming higher efficiency.

I did some calculations according to which using chemical energy one may get the heat from say burning sugar or dodecane or ethylene etc

and assuming 30% efficiency use heat engine -> mechanical energy and the 95% to electricity but even so the thruster will fly a couple of seconds only? Actually my calculations were for 100% efficient heat engine and 100kg or less total fuel most of which is sugar or oxygen in the case of dodecane.

Another problem is that unless the specific impulse is insanely high then a lot of gas will be lost with a thrust such as 1000 N or more. For example: 1900 N=9.8*200*x so the "x" here is the mass flow rate or in the example: 0.96 kg lost per second. For 1000 Isp it's 0.19kg and just 0.019 for 10,000 Isp, so it's linear simple calculation.

So it looks like the only way to power ion craft on earth will be using Helium 3 fusion? Which is impossible at the moment, if ever.