On the 9th June Elon Musk tweeted “SpaceX option package for new Tesla Roadster will include ~10 small rocket thrusters arranged seamlessly around car. These rocket engines dramatically improve acceleration, top speed, braking & cornering.”.
On the 12th June I tried to clarify Elon’s mysterious and exciting tweet with “... is this a curtain jet {2,{3,3},2} to create a momentary pressure reduction under the car?” but he is busy, so I thought that I would do some calculations for myself to check out the options.
From physics you will remember that friction is a fraction of the downward force on the tyres. So 1 newton downward force on a rubber tyre might give 1 newton of forward drive; you would only get 0.02 newtons if you had melting ice tyres. So we can do a simple calculation to tell us that the a boring Roadster, without the SpaceX option, is already relying on more than static mass and friction. If it accelerated at 9.8 m/s for 2 seconds it would not be going at 60 mph.
Other cars have done better than this. The historic data is plotted here http://www.mbtrusts.co.uk/DropBox/Historic Data.PNG (thanks to https://www.0-60specs.com/0-60-times/ for the data). The red line on the graph is for the boring Roadster.
If you have forgotten your physics then now is a good time to look at these videos that show that 'High pressures can be used to create low pressures' - demonstrated by perfume atomisers and also here https://commons.wikimedia.org/wiki/File:VenturiFlow.png https://www.youtube.com/watch?v=AUyczZ3EiZg )
I took the boring Roadster’s performance and tried to guess the suction under the car (I assumed that the suction force increased with the square of the velocity). I get the right kind of acceleration when we have a 4% pressure reduction as it gets to 60 mph. So I take that as my baseline.
Next, I plotted the achievable accelerations at different velocities for a range of reasonable suction levels (so when I say 2% bar I mean ‘boring Roadster suction increased by 2% of one atmosphere’). Amazingly even very small pressure differences involve enormous forces. The different curves are for different levels of suction. In the most extreme case the braking power appears unsafe for many drivers (A 10% pressure reduction might be hard to create? Not everyone is a racing car driver so I guess that they will limit it to 3 G anyway).
Using a mild design (a little bit of suction for one second). I have estimated the 0 - 60 time to be 1.2 seconds. I suspect that the thruster suction gets weaker at high speed (graph here http://www.mbtrusts.co.uk/DropBox/New%20Acceleration.PNG the thrusters turn off at 0.5 seconds).
I have attached my calculations here (http://www.mbtrusts.co.uk/DropBox/2018-07-01%20Thrust%20Estimate.pdf ). It would be great if someone could check them.
Yet another Elon Musk idea that is openly derided as ridiculous but actually seems to be possible.
Have fun
MESM
Elon’s original tweet ended with the comment that “Maybe they will even allow a Tesla to fly …”. If this post correctly interprets the thrusters then it might be possible to have secondary vents and active suspension that makes the car jump!
You might build the SpaceX option Roadster using three-nozzles left and right curtain and two-nozzles front and back curtain (= 10 thrusters).
I guess that the nozzles would point away from the centre of the car and down at ~30 degrees below the
horizontal. There is a small upward thrust from the nozzles but that is insignificant because a small suction is a big
(There is another refinement that is possible here. If the car normally had rubber flap flat against the base of the car then the thruster jets would temporarily suck the rubber flaps down and increase the suction under the car. When the thrusters stop then the flaps flip up again. My calculations do not assumed the rubber flaps.)
On the 12th June I tried to clarify Elon’s mysterious and exciting tweet with “... is this a curtain jet {2,{3,3},2} to create a momentary pressure reduction under the car?” but he is busy, so I thought that I would do some calculations for myself to check out the options.
From physics you will remember that friction is a fraction of the downward force on the tyres. So 1 newton downward force on a rubber tyre might give 1 newton of forward drive; you would only get 0.02 newtons if you had melting ice tyres. So we can do a simple calculation to tell us that the a boring Roadster, without the SpaceX option, is already relying on more than static mass and friction. If it accelerated at 9.8 m/s for 2 seconds it would not be going at 60 mph.
Other cars have done better than this. The historic data is plotted here http://www.mbtrusts.co.uk/DropBox/Historic Data.PNG (thanks to https://www.0-60specs.com/0-60-times/ for the data). The red line on the graph is for the boring Roadster.
If you have forgotten your physics then now is a good time to look at these videos that show that 'High pressures can be used to create low pressures' - demonstrated by perfume atomisers and also here https://commons.wikimedia.org/wiki/File:VenturiFlow.png https://www.youtube.com/watch?v=AUyczZ3EiZg )
I took the boring Roadster’s performance and tried to guess the suction under the car (I assumed that the suction force increased with the square of the velocity). I get the right kind of acceleration when we have a 4% pressure reduction as it gets to 60 mph. So I take that as my baseline.
Next, I plotted the achievable accelerations at different velocities for a range of reasonable suction levels (so when I say 2% bar I mean ‘boring Roadster suction increased by 2% of one atmosphere’). Amazingly even very small pressure differences involve enormous forces. The different curves are for different levels of suction. In the most extreme case the braking power appears unsafe for many drivers (A 10% pressure reduction might be hard to create? Not everyone is a racing car driver so I guess that they will limit it to 3 G anyway).
Using a mild design (a little bit of suction for one second). I have estimated the 0 - 60 time to be 1.2 seconds. I suspect that the thruster suction gets weaker at high speed (graph here http://www.mbtrusts.co.uk/DropBox/New%20Acceleration.PNG the thrusters turn off at 0.5 seconds).
I have attached my calculations here (http://www.mbtrusts.co.uk/DropBox/2018-07-01%20Thrust%20Estimate.pdf ). It would be great if someone could check them.
Yet another Elon Musk idea that is openly derided as ridiculous but actually seems to be possible.
Have fun
MESM
Elon’s original tweet ended with the comment that “Maybe they will even allow a Tesla to fly …”. If this post correctly interprets the thrusters then it might be possible to have secondary vents and active suspension that makes the car jump!
You might build the SpaceX option Roadster using three-nozzles left and right curtain and two-nozzles front and back curtain (= 10 thrusters).
I guess that the nozzles would point away from the centre of the car and down at ~30 degrees below the
horizontal. There is a small upward thrust from the nozzles but that is insignificant because a small suction is a big
(There is another refinement that is possible here. If the car normally had rubber flap flat against the base of the car then the thruster jets would temporarily suck the rubber flaps down and increase the suction under the car. When the thrusters stop then the flaps flip up again. My calculations do not assumed the rubber flaps.)