Would von Braun's Mars Landers Have Worked?

Fri, 24 Nov 2023 11:50:56 -0700

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Landing Boats

Wernher von Braun’s Das Marsprojekt envisioned a flotilla of 10 ships, operated by not less than 70 men, that would depart Earth orbit for Mars. Once at Mars, the transfer ships would remain in orbit while winged “landing boats” would fly as gliders down to the surface.

A von Braun Mars landing boat.

As if this weren’t already ambitious enough, the plan actually called for one boat to land with ski-type landing gear in the icy polar regions. Its crew would then unload earth-moving equipment, make the long trek down to the equatorial region, and construct an airstrip so that the other landing boats, equipped with conventional tricycle landing gear, could come down. (Presumably the bravest and most highly skilled men in the expedition would have been on the ice boat, as they would be landing on totally strange terrain with no chance of rescue!)

In Light of Current Knowledge

In computing the necessary lift and therefore the boats’ required wing area, von Braun considered the acceleration due to Martian gravity as about 38% that of Earth’s and the density of the Martian atmosphere as about 8% that of Earth’s.

Of course, much more is now known of Mars’ atmosphere than in 1952. In light of today’s knowledge, would von Braun’s winged ships have actually worked? Here’s a back-of-the-envelope calculation using the properties of the Martian atmosphere that are now known. (Note that atmosphere percentages may total slightly above or below 100 due to rounding and measurement uncertainty.)

Martian Atmosphere

Earth Atmosphere

From Moles to Kilograms

The Ideal Gas Law relates pressure, volume, amount of substance, and temperature as follows:

pV = nRT

wherein p is pressure (pascals), V is volume (cubic meters), n is amount of substance (moles), T is temperature (Kelvin), and R = 8.314 J/K·mol is the ideal gas constant. For a known temperature and pressure, the ideal gas law will predict the volume occupied by 1 mole of gas when algebraically rearranged as:

V = RT/p

Here is the relevant data:

The Ideal Gas Law therefore indicates these properties for the atmosphere of both planets:

Mars’ atmospheric density is only about 1% that of Earth! Von Braun, who estimated it at 1/12 that of Earth, was too optimistic by about 800%. This isn’t looking good for our landing boats … let’s keep going.

The Fate of the Boats

Von Braun’s landing boats had a wing area of 2810 m2 and massed 185 Mg. At 0.38 g, the required wing loading was therefore no less than 245 N/m2. (Surprisingly, this is about the same wing loading as a Piper Cherokee.) The design landing speed was 196 km/h (54.5 m/s).

How much lift would these wings have produced in the real Martian atmosphere? Well, the basic aerodynamic lift equation is:

L = CL½ρV2S

wherein ρ is air density, V is airspeed, S is wing area, and CL is the lift coefficient. (Lift coefficients are determined experimentally for given air conditions, body geometries, and angles of attack. The quantity ½ρV2 is also referred to as “dynamic pressure” or Q. If you’ve heard “max Q” called out during a rocket launch, this is the quantity they were referring to.)

Von Braun supplied a lift coefficient of 1.3, which he considered the optimum attainable with trailing-edge and leading-edge flaps. Using this coefficient and the other design criteria, I calculate the lift produced at Martian sea level by a landing boat at 336 kN, and therefore the wing loading at 120 N/m2: a pitiful 49% of the lift required for the boat to support its own weight!

What a letdown. It’s not enough that the real-world Solar System put a nail in the coffin of the cozy one envisioned in the Golden Age of science fiction (where we had web-footed friends on a jungly but habitable Venus or perhaps a stilted but cordial relationship with the Great Old Ones of Mars.) Even the rosy visions of mid-20th century science “fact” have now succumbed to the inexorable march of new knowledge.

Still … can you imagine?

Exploration of Mars, Chesley Bonestell

Topics: history technology