The ‘specific impulse’ of a rocket engine is one measure of its ability to convert the energy in its fuel into forward thrust. Its unit is ‘seconds’, and its measure could be interpreted as ‘how long could one pound of fuel produce one pound of thrust’.
If your rocket starts off 2/3rds fuel by mass, this will result in an average acceleration of 1g as the mass of the fuel is consumed.
The most efficient chemical rockets we have today have a specific impulse in the ~470 second range. The highest specific impulse thrusters of any sort that we have in wide use today are ‘ion thrusters’, which have specific impulses in the 50,000 second range (but can’t generate much thrust at all).
So 10-12 hours at 1g is about as much as we can do with existing hardware.
One very common misconception that higher specific impulse (ISP) is always good. Electric propulsion is different from chemical.
In chemical propulsion, you have the energy in the propellants. There higher ISP is better.
In electric propulsion, you use an external power source. Usually your propellant or reaction mass is inert, like Xenon. There, if you up the specific impulse but keep acceleration and delta vee the same, your power source mass increases. At some point your power source mass is a lot bigger than your propellant mass. Hence, your total mass for the same misaion would be less with lower specific impulse.
So in electric propulsion there can be too high ISP for a given mission and power source technology.
I've heard this before, but it seems to me that the 'problem' isn't the too-high ISP, but rather the heavy power source. For rockets, we've got the rocket equation which gives the exact fuel trade-off (carrying more takes you further, but also means carrying more weight). Is there a similar 'hard' relationship between ISP and power supply mass for electric drive systems?
Yes. Thrust is related to momentum while power to energy. So if you double the exhaust velocity, you double the thrust but quadruple the power needed.
P = 0.5 * mdot * v_ex^2
T = mdot * v_ex
A normal ion thruster might have ISP 4000 or 40 km/s exhaust velocity.
From the rocket equation, if our mission requires 10 km/s delta vee, mass ratio is exp(10/40)=1.28. So out of every 1280 kg, 280 kg is propellant.
If we have mass flow of 0.1 gram per second, thrust is 40000 m/s * 0.0001 kg/s = 4 N and power is 80 kW.
Acceleration is about 0.27 km/s per day. Not so good for humans through Van Allen belts. But fine for deep space propulsion.
80 kW of solar cells with 200 W/kg weight efficiency would weigh 400 kg. This is ISS level power.
So the spacecraft might have 280 kg of propellant, 400 kg of solar arrays, 600 kg of useful things.
Yeah, so my question comes down to 'how much can we play around with weight efficiency?' For example, maybe I can drop a lot of solar cells in exchange for a small battery or capacitor capable of providing the needed power for the higher exhaust velocity, but in bursts. Then we change the firing pattern from a continuous burn to alternating between burning and recharging the batteries, and save a lot of solar panel weight.
[on edit: the weight efficiency of the solar panels will also depend on where you are in the solar system...]
It would still just be the rocket equation no? The power supply mass that isn't ejected as energy in propulsion would just be counted as part of the rocket's dry mass (mf in the rocket equation).
GP is a nice reverse engineered explanation, but the actual origin of using seconds as a unit is to avoid having to compare metric and imperial units of speed. Isp is just exit velocity divided by g and it's conveniently in seconds, a pretty universal unit. And "one pound of thrust" only makes sense when you're in Earth's gravity field with gravity losses. Otherwise it's more precise to use Newtons for thrust.
> conveniently in seconds, a pretty universal unit.
Thankfully! Imagine if systems/cultures commonly differed in fundamental measures of time, just as they sometimes do for volume, distance, weight, etc.
For this kind of thing it's helpful to think about the dimensions and units involved.
In mechanics, "impulse" is a word for a unit of momentum. Momentum has dimensions (Mass * Speed), or (force * time), and can be stated in units of Newton-seconds.
"Specific" impulse is simply Impulse per unit mass of fuel (i.e. Newton-seconds per kilogram). The convention of stating it in units of seconds is based on Earth gravity (Newtons per kilogram).
If a system has specific impulse of 100 seconds, 1 kilogram of fuel would be able to accelerate a mass of 1kg at an acceleration of 1 G, for 100 seconds.
If I'm thinking about this correctly, the potential energy in the fuel isn't changing the net kinetic energy of the total mass, it's just re-distributing it between the vehicle and the exhaust.
Total momentum is conserved, but distributed: the individual momentum of the vehicle and the exhaust jet will be of equal magnitude and opposite direction (assuming a straight line), so if the rocket started in free space at rest (zero momentum), after it's run for a while the exhaust jet and vehicle will have equal and opposite momentum vectors.
Energy is a different thing, but related to specific impulse. In a perfectly efficient system (not what really happens), the decrease in stored energy within the fuel tanks would be equal to the increase in total kinetic energy (i.e. the sum of vehicle and exhaust kinetic energy).
50,000 seconds would be 13.89 hours, though I’ll grant you “with existing technology” would preclude getting enough electrical power into an ion drive for that to do one whole gee.
If your rocket starts off 2/3rds fuel by mass, this will result in an average acceleration of 1g as the mass of the fuel is consumed.
The most efficient chemical rockets we have today have a specific impulse in the ~470 second range. The highest specific impulse thrusters of any sort that we have in wide use today are ‘ion thrusters’, which have specific impulses in the 50,000 second range (but can’t generate much thrust at all).
So 10-12 hours at 1g is about as much as we can do with existing hardware.