One item of contention that I’ve seen in the emerging space industry is about the relevance that suborbital spaceflight has for future orbital applications. With the exception of RpK, all of the current effort going into building reusable, safe, and operable launch vehicles has been focusing on suborbital vehicles first. However, while most of those companies are focusing on suborbital vehicles at first, and while most of us think we can close our business cases on suborbital, most of us fully intend to proceed on to orbital spaceflight if we can make a successful enough go at our first markets. That is one thing that MSS, XCOR, Armadillo, Blue Origin, TGV, SpaceDev, Canadian Arrow all have in common.
However the conventional wisdom in the industry is that orbital launch requires X times more energy (where X is a number that varies from 25-81 depending on who is throwing out the number) than suborbital launch, so suborbital launch really is an entirely different problem. While I will admit that suborbital spaceflight is a more benign flight regime in many ways, this particular piece of common knowledge is misleading at best, completely bogus at worst.
The origin of these numbers is the simple kinetic energy equation KE=1/2*m*v^2. Since kinetic energy is equal to the square of velocity, if you need 5 times more delta-V to get into orbit than to reach 100km, you end up needing 25 times as much energy.
The problem is that this is wrong. You don’t need 5 times as much delta-V to get into orbit as you do for a suborbital vehicle. Or to put it more correctly, people making this argument don’t seem to have a good handle on how much delta-V it really takes to make it even to 100km.
I can see where such people are probably making their mistake. If you take an extraordinarily naive first brush attempt at estimating the delta-V requirements for a 100km suborbital hop, you might just determine what cutoff velocity you would need to coast up to a 100km apogee. If you run the numbers it comes out very close to 1400m/s, which is about 1/5th of the theoretical minimum orbital velocity.
What both of those numbers (that for the suborbital delta-V requirement and for the orbital delta-V requirement) both ignore is air drag losses and “gravity losses”. If we lived on a planet without an atmosphere, and if we had engines with infinite thrust-to-weight ratios, they might have a point.
Real world orbital launch vehicles typically need to deliver 8500-10000 m/s of delta-V (compared to the orbital velocity of ~7200m/s) to reach a low earth orbit. Somewhere between 1300 and 2800 m/s of delta-V ends up getting eaten up by drag and gravity losses.
To illustrate gravity losses, imagine a vehicle just after takeoff. It has a thrust to weight ratio of say 1.2 (about what Saturn V was IIRC). That means that at that point, 1/1.2=~83% of the rocket’s thrust is just going into counteracting gravity. As an orbital vehicle gets out of the thickest part of the atmosphere, it quickly starts turning so it can start accelerating horizontally (most of reaching orbit is going fast enough sideways that you can fall without ever hitting the ground). If your engine is firing parallel to the ground, you aren’t suffering any gravity losses because your engine isn’t fighting against gravity. You are falling however, so you either need to get up to a sufficient height before you make that turn (called “lofting”), or you need to fly with your engine not quite parallel to the ground (so a tiny bit is providing some lift). But basically for orbital vehicles almost all of their drag losses occur very early on since they spend most of their flight flying horizontally. For a straight up and down suborbital flight, you might not have much higher gravity losses in nominal terms than an orbital launch vehicle, but as a percentage of the overall delta-V suborbital vehicles take a much bigger hit.
Drag also tends to impact suborbital vehicles (and reusable ones in particular) more than an orbital launch vehicle. Drag tends to scale with the frontal area of the vehicle. However, the mass tends to scale with the volume of the vehicle. If your vehicle was spherical with a radius of r, the force due to drag would scale with r^2, while the mass would scale with r^3, thus the acceleration due to drag would scale with 1/r. Basically smaller vehicles suffer much worse drag penalties than bigger vehicles. Another issue with suborbital vehicles (especially VTVL ones) is that they tend to have much squatter aspect ratios compared to orbital vehicles. Take a look at your average orbital launch vehicle, like Atlas or Delta. They are typically about 12-15x as long as they are wide (Ares I is a whopping 25:1!). Due to landing stability issues for VTVL vehicles, you’re more likely to see aspect ratios of around 3 or 4 to 1 for single stage vehicles and 6 or 8 to 1 for orbital vehicles. Squatter vehicles tend to have much higher drag losses than longer skinnier vehicles, since they have more frontal area per unit mass. Between those two issues, and the fact that suborbital vehicles spend a lot larger percentage of their flight duration inside the sensible atmosphere, and you once again end up with drag losses accounting for a much higher percentage of the delta-V required for a suborbital vehicle.
The real eye-opener for me came when I tried to toss together a quick “1DOF” trajectory model a couple of days ago. The model included drag and gravity losses, with an exponential curve fit model for the atmospheric density at various altitudes. I ignored the performance increase you get at higher altitude (due to less backpressure losses), and just picked a “mission average Isp). I assumed an average drag coefficient (for the shapes we’re interested in, the drag coefficient doesn’t change too drastically over the various Mach numbers in question). To try out the model, I put in some numbers for a vehicle that was roughly equivalent to what you would need to compete in Level 2 of the lunar lander challenge (with a huge amount of reserve propellant). I was expecting to see us get close to 100km with it, since the design had a delta-V of over 2km/s. Instead of 100km, my model showed the vehicle peaking out at only ~25km. Even doubling the propellant mass while keeping the dry mass constant wasn’t quite enough to make 100km.
The basic takeaway was that a ground launched VTVL RLV is going to take a pretty sizeable delta-V in order to actually make it even to 100km. While I didn’t keep going on trying to see what it would take (since I had to get back to work), it looks like you might need 3-3.5km/s of delta-V just to reach 100km in real life. If you’re trying to go to higher altitudes (as most of us are), you need even more delta-V.
Now, some may say that this still is only 30-40% of the delta-V needed to reach orbit, and that therefore you still need 6-9x as much energy to reach orbit, but even this is missing something important. Most orbital launch vehicles are “two-stage to orbit” vehicles, and most orbital RLVs will also be TSTO. If your first stage has 3.5km/s of delta-V with a payload equal to the fueled mass of your upper stage, and it also has 3.5km/s of delta-V, you’ve got 7km/s of delta-V overall. Which is between ~75-80% of the velocity you need to reach orbit. Which means a big VTVL “barely suborbital” vehicle with a much smaller “barely suborbital” VTVL vehicle stacked on top is going to have over 66% of the energy needed to reach orbit.
But 1.5X just doesn’t sound as impressive as 25X does it?
Now, before I wrap this up (which I need to do soon since this post has spilled over into Sunday morning), I want to add a few caveats. First off, I don’t know how the numbers pan out for ground launched HTHL vehicles. I know XCOR does, but doing a real analysis of an HTHL suborbital vehicle requires more than a simple 1DOF. My guess is that the basic conclusion, that the amount of delta-V you need to reach 100km ends up being a large fraction of the delta-V you would want out of a first stage of a TSTO orbital RLV, still holds.
Second, air launched suborbital vehicles take much smaller hits from drag losses, and can get away with much bigger expansion ratios. Which means they can get away with propulsion systems that tend to be lower performance (both from an Isp standpoint and a mass ratio standpoint) than ground launched RLVs. It also means that the delta-V required for being “barely suborbital” is lower, and hence you can build a suborbital RLV that actually is much, much lower performance than a comparable TSTO first stage. So, maybe some of the original criticism is fair–if you’re talking about air launched suborbital RLVs.
Third, there are lots of issues other than raw delta-V performance that are more challenging for orbital vehicles. TPS is one of them. Figuring out the logistics of how to recover 1st stages that land down range (or how to make them high enough performance to be able to do a Return to Launch Site landing). How to handle vehicles that are physically bigger. Etc.
But in spite of all those caveats, the conclusion you should walk away with is that suborbital vehicles really aren’t “dead ends” that have no relation to the challenges of orbital vehicles. They may deliver slightly less performance than an orbital launch vehicle stage, but the real energy difference may only be a factor of 1.5-4x, not 25x.
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