Pebble Risks and Thrust
As promised (
@Pmac727 and
@Joerg ), I have looked at the possible exhaust velocities of the curtain and thrust versions of the SpaceX options package. My preferred thruster model is still the suction model (as you will know by now!) but I also cover the ‘thrusters-as-rockets’ case too.
(Feel free to contact me for my calculations – comments are welcome)
I break the problem down like this (and I used Wikipedia a lot!):
- What is the velocity of the air in the suction curtain (this is the model that I prefer)
- What is the average velocity of the thruster exhaust (if all the stored energy were to be used as a rocket – I do not prefer this model)
- How fast would a granite road pebble go if it fell across the nozzle in each of those two cases (suction and rocket)
The air curtain looks a bit like this:
The Bernoulli effect gives the appearance of suction as illustrated below:
(Step 1) For the performance shown earlier in this post I need 2% suction and that means that the curtain air velocity needs to be ~57 m/s (about 129 mph assuming an efficient design).
The velocity of the exhaust nozzle could of course be very very high if you simply cut a hole in the side of the COPV so we can easily imagine initial exhaust velocities of 1,500 mph, HOWEVER I was really surprised when I tried to calculate the potential energy in the COPV and the kinetic energy in the exhaust stream.
I looked at what happens when the COPV is filled with compressed air. Air gets hot when it is compressed and if the Roadster compressed air to 5,500 psi without cooling then the temperature would get to more than twice the melting point of aluminium. Obviously, there must be a cooler that makes sure that the compressed air is cooled before it goes into the COPV.
So, for isothermal compression (getting rid of the compression heat) the total potential energy in one ‘Super-Draco’ COPV is ~1.9 MJ (about 0.55 kWh/ 0.47 kg TNT).
(Step 2) Unexpectedly, decompressing the air in the rocket version of the thrusters is disappointing if you cannot warm the air first because the air gets very cold and does not expand as fast as you want. I believe that there is not enough time to warm the air (the car would have to heat up 54 kg of air in less than 2 seconds without slowing it down – while it is still in a pressure vessel/ heat exchanger). If we take all the potential energy and convert it evenly into exhaust kinetic energy at 100% efficiency (ha ha) we get:
- 54 kg of air
- 189 m/s (423 mph)
We are ready for step 3. I read about road gravel and I have chosen a 14 mm diameter granite pebble with a drag coefficient of 0.47. I get these results for the pebble velocities:
- Suction curtain/ 30 cm wide curtain – pebble ~4.5 m/s (10 mph)
- Rocket style thruster/ 30 cm exhaust plume – pebble ~15 m/s (33 mph)
- Rocket style thruster/ 90 cm exhaust plume – pebble ~26 m/s (58 mph)
In conclusion, I was quite surprised by the results:
- The curtain pebble velocities are safe
- The rocket thruster pebble velocities are scary but not too dangerous
Finally, if you are not worried by the ‘thruster rocket design’ spewing out 54 kg of air at > 400 mph then you will be encouraged to hear that that has enough kinetic energy to get the Roadster to more than 60 mph! (Using a horizontal-type rocket thruster/ I have assumed that the Roadster is 1,814 kg).
……………………………………………………………………………………………………………………………………………………….
So, I have been talking about the car’s peak performance, but as a side-issue we should bear in mind that a cooling bleed for the car would have a huge impact on the car’s high-speed endurance on a track. The cooling bleed would cool the batteries, electronics, and engines: