Today I came across an article about Spin Launch , a secretive startup working on spinning a payload to supersonic speed to get a ballistic first stage launch boost thus lowering the size and cost of the rocket booster needed to get to orbit.
Having seen other ideas of accelerating to orbit on a rail gun before, and knowing how huge centrifugal forces can be, I found the idea of spinning very disturbing due to the massive centrifugal force that will be created on the payload virtually crushing it or any delicate payload inside it.
So as I sat waiting for my dry cappucino, I decided to quickly do some math using the angular velocity vs force formula to see how big the diameter has to be of the spinner to make sure you get no more than 10 g of centrifugal force to accelerate to just about speed of sound of 333 m per second.
Shockingly that turns out to be a circle of 2 km (1.65 miles) diameter!
And if you want to accelerate 3 times that speed the diameter grows by square so 9 times of that !
This follows from the formula that the radius = velocity^2 / (Max angular acceleration allowed) - (1)
But here is the good news. Instead of trying to build a cyclotron if you simply had a straight linear accelerator rail that can accelerate at 10g, you only need 3.33 seconds to accelerate to speed of sound (approx 333 m /s) resulting in a rail of only 500 m or half a km in length! That's tiny! (S = 0.5 x a x t^2) - (2)
And if you want to go 3 times faster using this method you also need a length 9 times longer but it's only a manageable 4.5 km and no crazy circles. Moreover you can angle the ending part of ramp gently to make sure you release payload at an increasing altitude.
In many flat deserts this would be very easy to accomplish. And no crazy engineering to build a smooth circle !
So why is this company doing it the wrong way? Well my guess is they decided to only support payloads that can handle 1000 gs or more. Notice that in equation (1) one saving grace is that if you keep the velocity fixed and decide to shrink radius then 10 times smaller radius only increases force by 10 times.
So a 100 g would require only 200 meter cyclotron
And a 1000g limit would require only a 20 m diameter device to accelerate payload to 333 m/s.
So my guess is they are building this tiny centrifuge of few meters in diameter to launch tiny payloads that are really robust on crushing and launching them on tiny second stage rockets and letting their customers know to expect 500+ gs.
May work for some payloads but clearly they must be planning larger circles and straight lines in their secret roadmap to have any hope of competing with ever cheaper traditional launchers or even space ship 2.
