It’s Monday! Let’s talk about specific impulse.
Specific impulse (otherwise known as ISP) is to spacecraft what miles-per-gallon is to your old internal combustion engine car. It’s fuel efficiency. ISP is what determines how much push (or, formally, “impulse,” measured in Newton-seconds, N*s) you get for every kilogram of fuel you carry, and your total amount of pushing capacity divided by your mass gives you the all-important metric: delta-v.
First, we must digress for a while into delta-v, because it really is all-important.
Delta-v literally means “change in velocity” and it is measured in meters per second, but to carry the analogy further, if ISP is miles-per-gallon then delta-v is the total range you have from a full tank of gas. Since there are no gas stations in space (yet), spacecraft can never refuel. They have to get wherever they are going with only one tank of gas, i.e. a specific, finite amount of delta-v. Your delta-v determines where you can go and where you can’t.
(Above: A map of the delta-v needed to travel the solar system from Earth; add up the numbers from between each of the dots on the path to the place you want to go, and you get the total delta-v needed to get there. Note that this map assumes that you make each trip during a good orbital alignment, and use an efficient transfer trajectory, so the resulting numbers are close to the minimum possible. Also note that the highest delta-v ever achieved by a spacecraft under its own power was the Dawn mission, which only did about 11,000 m/s; that means we’ve never even built a spacecraft capable of flying on a direct course to a Mercury intercept.)
You can get more delta-v a few different ways. You can carry a bigger gas tank, so you have more gallons to burn. You can make the engine more efficient (higher ISP), so you get more miles (or more m/s) from the same number of gallons. Or, for spacecraft, you can make the whole spacecraft lighter, so that each unit of push (impulse) causes a larger change in velocity. (The analogy was bound to break down somewhere, but you could think of this kind of like a street racer throwing out the rear seats from his car to improve his quarter-mile time by a quarter second or so because the engine now has less mass to move). Lastly, you can sometimes get extra delta-v by using gravity assists; the Parker Solar Probe, for example, will spend a total of 7 years to perform 24 separate gravity assists at Venus and reach a top speed of almost 200,000 m/s. (Since we’ve already thoroughly butchered the analogy, this is kind of like rolling your car downhill in neutral to pick up extra speed without spending extra fuel, but it unfortunately requires the hill to be in the right place to take you where you want to go – In space terms, the planets literally have to align, which may add years to mission timelines).
So, is more delta-v better? Well, generally, yes. But, there’s a difference between the general answer and the way we actually do things. In practice, delta-v is so limited that we design each spacecraft custom, have it carry pretty close to exactly the amount of delta-v it needs, and no extra. We do this because carrying extra costs money, and we know we will only use the spacecraft once, and then throw it away, so why spend the extra money? Think about this dynamic: You want to send something to Jupiter? You spend a few billion dollars and about 10 years developing the specific super-high-performance thing that can fly the specific trajectory that can barely make it to Jupiter. You build one copy, it flies one mission, done. It is billions well spent in my opinion (looking at you, Europa Clipper!), but admittedly not very capital efficient.
[Basically, we are custom-building a single Lamborghini, driving it one time, and then throwing it away.]
This is significantly different from the way you actually want things to be in a healthy industrialized space economy. Take semi trucks as the Earth-based example. You design a semi truck, and that truck can travel all the roads of the world. It has a maximum cargo capacity for any given journey, but this one design can achieve nearly all journeys that fit within that cargo capacity. So, you build a few hundred thousand copies of the same truck, drive the cost down with scale, and they serve as multi-purpose vehicles doing numerous different tasks over many years of operational life. They get re-used, and can be re-used for whatever the owner wants.
[Building these by the thousands and reusing them would be better.]
There are two advantages that a semi truck has over an interplanetary spacecraft. First, infrastructure. On roads, gas stations exist, so refueling and re-use are commonplace and assumed to be possible by the semi designers; the capability is built in, and the world is such that it can be used. Second, margin (which is related). Any given leg of any semi truck journey will be well within the range that the semi truck has on one tank of gas. Another way to think of this is that gas stations are common enough that the semi will pass many of them before needing one. There’s plenty of margin for error – you can drive 100 miles, or 300 miles without worrying, because you have plenty of fuel.
In space, nobody has plenty of fuel. You have enough fuel to do one mission. There’s no physical way to build a spacecraft that has enough fuel to do “whatever the owner wants” in the solar system. It’s very bloody hard to even do one mission (to the point where our flagship space missions will literally spend years looping around various planets for gravity assists because they can’t carry enough fuel to fly direct), let alone come back to Earth, let alone bring back souvenirs or cargo. We’d love more delta-v, but we don’t have it, so we build like we don’t have it. There are no semi trucks in space yet, not because we don’t want mass-produced generalist space vehicles, but because we literally can’t build them with current technology.
Okay, enough about delta-v. Back to ISP.
ISP is basically exhaust velocity (officially, it is the exhaust velocity divided by the acceleration of gravity at the surface of Earth, so, meters/second divided by meters/second^2, which means the units for ISP are just seconds, which I personally always found very confusing). Think of basic physics – Force = Mass x Acceleration (F=m*a). The exhaust coming out the back of a spaceship has mass. The faster it shoots out, the more it has been accelerated, so the more force it applies to push the ship forward. So, anything that helps us shoot mass out the back of a spaceship faster will increase ISP.
[Basic rocket science at work.]
Baseline, you can just use gas pressure, if you want, and fly around like Wall-e with his fire extinguisher (cold gas thrusters). You can accelerate your fuel mass much more by combusting or exploding it (a chemical rocket). You can also accelerate it even more by getting it really hot in a nuclear reactor (nuclear thermal propulsion), since heat is basically the same thing as speed. Or you can make your fuel electrically charged, and accelerate it super fast using an electric field (electric propulsion, mostly ion thrusters).
[Much better rocket science at work. This is NASA’s NEXT ion thruster, probably the best ever flown to date.]
The range of ISP for chemical rockets goes up to about 450 seconds. The range for nuclear thermal propulsion is expected to get up to about 900 seconds, though nobody has built these yet. The range for ion thrusters is usually up to about 4000 seconds, but if you talk to the ion engine guys at NASA they will tell you. basically, “We can make the ISP as high as we want.”
All of this needs a bit of unpacking, especially that last bit. Earlier, I said increasing ISP could increase delta-v. I also said that we have no way to get enough delta-v to make generalist cargo spacecraft that fly wherever we want in the solar system a thing. And, I just said we can make ISP as high as we want, but instead of doing that, we stick to 4000 seconds or less.
But, if you can make ISP as high as you want, can’t you make delta-v as high as you want?
Well, no.
See, there are other forces at play, mainly electricity. With a chemical rocket, you store all your energy in the propellant itself, and unleash it with a chemical reaction; all else equal, higher ISP is always better (though all else is definitely not equal, for reasons to be explored in a later issue). With electric propulsion, though, your propellant doesn’t store much energy at all – it’s just a compressed gas (typically). The energy is from electric power, which your spacecraft needs to generate. The ISP depends directly on the voltage of electric field you use to accelerate your ions – more volts, more ISP. Usually, systems use between 300 V and 2500 V, but engineers on Earth can easily build electrical systems that get up to 10,000 V, and some laboratory electrostatic systems even go up to 25,000,000 volts, and shoot ions through at very close to light speed. That’s what the NASA people mean when they say they can make ISP as high as they want: we can make the accelerating voltage super high if we feel like it, and that makes the exhaust velocity insane.
But, the equation for the velocity of an ion after acceleration from an electric field is v = Sqrt(2qV/m), where v is velocity, q is the ion charge, V is the voltage of the potential the ion accelerated through, and m is the ion mass. The thing to notice is that pesky square root.
Remember back to F = m*a? If I want to increase my force (F), I need to increase either the mass I throw out the back, or increase the acceleration I apply to that mass. With an ion thruster, to increase the mass, I use a heavier fuel gas, and to increase the acceleration, I apply a higher voltage. But, because the velocity of an ion is related to the square root of voltage/mass, two things are true:
- If I increase my fuel mass, I get a linear increase in my force for a given exhaust velocity, but my velocity will decrease with the square root of the mass. If you think through those two trends, you find that higher mass ions are better because each additional increment in mass causes less velocity reduction than the last, while the increase in mass stays linearly beneficial to force; this is why xenon (a very heavy gas) is the king of the ion fuels.
- If I increase my voltage linearly, I only get a square-rooted increase in my ion velocity – each incremental volt costs me the same amount of electrical power, but has exponentially diminishing returns in terms of thrust.
So, voltage has diminishing returns, but it still has returns, right? So why not just stack voltage like NASA says we can? Well, because the power to generate that voltage has to be produced on the spacecraft, usually with solar panels, and solar panels have mass. So adding voltage adds more mass to the spacecraft, and does it pretty close to linearly. If I add dry mass linearly, but get exponentially diminishing returns in thrust from that added mass, eventually I will hit a maximum in delta-v, where increasing my exhaust velocity starts to add mass so fast that total delta-v actually decreases.
And that’s why NASA doesn’t fly anything with more than about 4,000 seconds of ISP: It would be stupid.
So…. this is in the vein of me admitting my early naivete in this space. When I started designing our ion thruster, I was thinking like a chemical rocket designer – more ISP = good! So, I designed it to run at about 27,000 seconds of ISP. This sounded super awesome – the math showed that you could fly a 12-unit cubesat to Mars and back on 1 kg of fuel! That’s pretty cool, and I talked about the possibility a lot in my early presentations about the tech.
And, the truth is that, yeah, you could do it, but it would require fully half the mass of the spacecraft to be just solar panels to run the engine, and it would take you like 6 years to fly the trip. If you cut the ISP in half, and carry 2 kg of fuel, you can either shave two years off the trip (give or take), or cut half your power requirements and add 30% to your payload mass allotment. In other words, it was a stupid design. It sounded flashy to investors, and made a good talk at conferences, but people who actually understand ion thrusters deeply know better.
Eighteen months ago, I didn’t know better. I learned. Now, hopefully, dear readers, you have learned too.
This leads to a couple different conclusions. First, if power = mass, then I REALLY care about the power density of my power supply. More watts/kilogram results directly in higher optimal ISP, and higher maximum delta-v, which both opens the gates to more destinations in space and enables more of a spacecraft’s mass to be dedicated to cargo on all the trips we can barely run now. That moves us a bit further from single use Lamborghinis and a bit closer to reusable semis.
Second, since nuclear is coming, and ultra-light-weight solar panels are coming, demand is about to exist for much higher ISPs than we’ve flown to date. Ion thruster development needs to shift to prepare for that transition. That’s one of the things we are thinking about in our design work here at Orbital Arc.