Well That’s The End of That (Moonies I)

It’s July. Time to sit in the shade, and be economically productive more than calorie destructive. It’s also the month where North Americans contemplate “a great nation,” whichever of those you sit in. Let’s contemplate the Augustine Report, or formally, Seeking a Human Spaceflight Program Worthy of a Great Nation. One of the Augustine Report’s takeaway points? Stay out of gravity wells!

Take the example of early lunar probes. The US first sent the Ranger program, to gather mapping imagery, then the Surveyor program, to perform geologic studies. Ranger probes took television stills on the way to their (fatal) impact, while the Surveyors made soft landings, survived, and returned data.

The last, successful Ranger probes weighed 804-809 pounds (~366 kg) at Earth departure. Some of that (several kg) was trim propellant, for a midcourse correction. With no trim burn on the outbound leg, the odds of hitting the Moon- based on launch vehicle accuracy alone- were low. Surveyor 1 and 2, designed just a year later, were 596 lb (271 kg) in landed configuration, but 1970-1980 lb (~895 kg) in flight- a difference of 1374 lb (~620 kg), almost all propellants. That’s right, Surveyor wasn’t just more propellant than probe- it was over twice more!

This difference is due to the Moon’s strong gravity. Things want to fall into the Moon at speed. And yet, lunar gravity isn’t enough to hold any appreciable atmosphere. Parachutes, wings, rotor blades, etc. do absolutely nothing. Things that have to land on the Moon, and not crash, then need to brake themselves with only one thing: propellant, and lots of it. Surveyor was built around a big, solid rocket casing that did the primary retro-burn. That motor case then dropped away, and three smaller, liquid-fueled thrusters finished the job. The Moon’s gravity is so strong, not only was half a ton of propellant consumed, but the casing alone was enough that it was dropped to lighten the craft. More braking mass also means more propellant needed to do midcourse corrections as a knock-on effect.

We can keep going- NASA did. The Apollo Program’s Lunar Module weighed 33500 lb (~15100 kg) in descent configuration, and under half that (14800 lb, ~6840 kg) landed. That’s 18000 lb (~8248 kg) of propellants burnt right up. The Lunar Module Ascent Stage then ignited at 10500 lb (~4870 kg), ending up at 4800 lb (~2145 kg) in orbit (plus some reserve fuel). All told, the full LM went from 33,500 lb (15,103 kg) to around 4900 lb (~2250 kg), a drop of nearly seven times. This should clearly illustrate that round trip through a gravity well is an even bigger loss. You not only need propellant to enter, and propellant to leave. What’s even worse, the inbound propellant is braking your outbound propellant… and all that inbound fuel is braking itself to a lesser degree, requiring more course correction fuel, and structure, and further effects.

In manned missions, the risk tolerance is far lower, so a safety margin is designed into everything. In particular, the outbound fuel is padded higher, which means inbound fuel goes higher at a faster rate. Which means the launch vehicle grows bigger at an even greater multiplier. In the Apollo case, its Saturn V rocket was originally planned to have four F-1 engines. As planners fleshed out the Apollo designs, the Saturn V had to grow to five engines, mostly due to “the damned LEM,” said von Braun.

These multiplier or cascading effects are due to the Tsiolkovskiy Equation or Rocket Equation:

Delta V = Isp ln M/m

Here, Delta V or dV is the change in your speed; Isp is specific impulse, a measure of the efficiency of a rocket engine. ln is the natural log of M/m. M is the starting mass of the vehicle (that is, full of propellants), and m is the ending mass (out of propellant). M/m is then called “mass fraction”- the amount of the vehicle that is propellant.

Obviously, the mass goes down, just like in a car. But unlike a car, dV is around a kilometer per second (~2200 mph), depending obviously on the trip. Given that useful rocket engines here have an Isp of 200-440 seconds (~3000-5000 m/s), mass fraction is around a quarter to a half. In other words, not like a car at all… unless at fillups, you fill the tank, the trunk, the backseat, etc. Talk about pay-at-the-pump. And that’s the Tsiolkovskiy breakdown for the lander stage only. The equation needs rerunning to get a mission to the Moon in the first place- a higher dV. This was already obvious in the ’60s.

Upshot? Don’t enter a gravity well if you can avoid it.

…if you can’t avoid it, a flyby or impactor probe avoids retro-fuel mass, and thus cost.

…if you can’t avoid that, a hardlander saves versus a soft (manned) lander.

…if you can’t avoid that, at least go on a one-way trip.

Better yet, avoid the lunar gravity well for… a small body! I’ll keep explaining why.

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