# Gravity on Von Braun Station

Quote of the Day

Late to bed, early to rise, work like hell, and advertise.

— Wernher Von Braun, a saying he kept on his desk. He was not going to repeat the mistakes of other rocket pioneers who shunned publicity.

Figure 1: Wernher von Braun. (Wikipedia)

I have been reading about Wernher von Braun's work with Disney on popularizing the idea of spaceflight with the public. He was a genius at marketing and a tireless champion for space flight. In addition to his television work, he also gave numerous speeches to any group that would listen. I smile as I think about my high‑school physics teacher beaming with pride when he spoke of von Braun arriving in a helicopter to speak to local physics teachers about space and flying to the moon. My physics teacher could not remember the details of what von Braun spoke about, but his entrance and exit in a helicopter made a huge impression on a town of 1800 people!

Figure 2: Collier's Magazine Cover. (Source)

In addition to his work with Disney on animating spaceflight, he also worked with the legendary space artist Chesley Bonestell on a Collier's magazine article that people still marvel at for its visionary portrayal of spaceflight (Figure 2). He really made spaceflight seem possible.

He even tried writing a novel about spaceflight called Project Mars: A Technical Tale, which is available for free from the Internet Archive. I read the book and it was a slog. I will say it had the most mathematics of any novel I have ever read. The appendix is intimidating.

The early work of von Braun put great emphasis on a space station that rotated to create artificial gravity, which he described in detail in the Disney video shown in Figure 3. This space station concept is often referred to today as von Braun Station. In the video, he says that the space station is wheel-shaped with a 200-foot diameter and that it rotates at 3 revolutions per minute. This is enough information for us to calculate the amount of gravity that the station's occupants will experience.

 Figure 3: Von Baun Briefing on His Space Station Concept.

We can compute the level of artificial gravity generated by the space station using the equation for centrifugal acceleration under circular motion (Equation 1).

 Eq. 1 $\displaystyle {{a}_{c}}=\frac{{{{v}^{2}}}}{r}=\frac{{\overbrace{{{{{\left( {r\cdot \omega } \right)}}^{2}}}}^{{{{v}^{2}}}}}}{r}=\frac{{{{{\left( {r\cdot 2\cdot \pi \cdot f} \right)}}^{2}}}}{r}=4\cdot {{\pi }^{2}}\cdot r\cdot {{f}^{2}}$

where

• ac is the centripetal acceleration (artificial gravity).
• r is the radius of the space station.
• f is the rotation frequency.
• ω is the angular frequency.

We can compute the level of artificial gravity as shown in Figure 3.

Figure 3: Calculation of Space Station Acceleration.

So this space station concept would generate ~30%⋅g. This level of gravity is similar to that of Mars, which has 38% of the surface gravity of Earth.

I should mention that a very limited experiment with artificial gravity was attempted with the Gemini 11 mission and the Agena docking target they were using for practice. The experiment generated only 0.0005 · g (link), but it was a successful test (note that some sources report 0.00015.· g).

Figure 4: Gemini-Agena Artificial Gravity Experiment.

We can confirm the level of gravity generated with the calculation shown in Figure 5.

Figure 5: Gemini Gravity Calculation.

Figure 6 shows a photo of the Agena tethered to Gemini 11.

Figure 6: Agena Tethered to Gemini 11. (NASA)

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### 6 Responses to Gravity on Von Braun Station

1. Malcolm Frame says:

"...equation for centrifugal acceleration under circular motion..."

Probably a typo, but it should read "centripetal acceleration"

• Craig McComas-Shelton says:

Actually, I believe centrifugal is correct. This is because the artificial gravity is created when the spin of the station generates acceleration away from the center, causing an outward force on any mass, like the inhabitants.

This also reminds me of an interesting article I read in Popular Science (https://www.popsci.com/earth-spin-faster/) discussing the effects of Earth's rotation speed changing, thereby altering the balance between the centrifugal and gravitational forces exerted on masses. It specifically mentioned the effects it would have on the oceans, causing water levels to rise around the equator and drop near the poles as the rotation speed increased.

2. Robert Murphree says:

I remember the space station shows on disney hour on tv in the 1950's. And werner von Braun Duck ever since that on disney. I am almost ultimate nasa and astronomy nerd since 1960s. I am fine with military and space and science associations and the cold war. Caltech BS 1974.
The WWII story in Walter McDougal's "...and the Heavens and the Earth" political history of space" gives the truth on Von Braun, underground factories for v1 and v2s, manned as part of slave labor concentration camp that never saw the light. 100's -1000's dead left lying in the caves.

• mathscinotes says:

Thanks for the reference. I have put it on my reading list. The Dora concentration camp (link) was a nightmare.

You can argue much of our modern high-tech infrastructure had military funding at its inception. Look at the history of Silicon Valley and the manufacture of electronics during WW2.

mark

3. Robert murphree says:

Cold War competition produced some of our best work: the peace corps, foreign aid, etc. after almost losing the war by being unprepared, Eisenhower in “crusade in Europe” said democracies should work together to fight bullies like ISis and make sure every soldier is well trained before war. The failure of Pearl Harbor drove intelligence agencies growth. But Eisenhower’s fear in the military industrial complex was well placed. Mcdougal’s point was that as the economies of scale become ever larger, they develop their own political constituency that bends the choices on a technology away from the needs of mankind and towards the technocratic incrowd. A lot of it departments are examples.

4. Robert Murphree says:

rotation of the earth affects the shape of the earth, the geoid. fatter radius at the equator and shorter at the poles
https://www.esa.int/Applications/Observing_the_Earth/GOCE/A_force_that_shapes_our_planet