[AR] Re: Tesla Thruster Specs?
- From: Peter Fairbrother <peter@xxxxxxxxxx>
- To: arocket@xxxxxxxxxxxxx
- Date: Sun, 22 Sep 2019 08:29:18 +0100
On 20/09/2019 21:01, Peter Fairbrother wrote:
On 20/09/2019 19:59, Henry Vanderbilt wrote:
Don't forget they say there will be ten thrusters distributed around
the car. If four 400 lbf thrusters can take useful
lateral-acceleration part in a given tight turn, that's about .4G
additional turn force. Quite significant in sports car terms; ~1G
lateral acceleration is typical, somewhat higher with arrangements for
aerodynamic downforce to increase available tire grip.
Elon is probably talking ~3G total; ~1G of that will coming from the
tires - possibly significantly more if some of the thrusters are
adding downforce.
I had imagined it was all used for downforce - there is power to spare
(1MW+!) in the electric motors, and with a low-mass high-power car the
big problem is downforce...
Hmm, maybe not - some rather ridiculous 0-60 mph bote numbers:
assumptions: 2000kg car / 1MW delivered power / 1.5 coefficient of tyre
friction / 5G limiting acceleration / 700Ns/kg air rocket Isp
The first problem with an electrical drive car is traction; even a F1
car with double the power-to-weight ratio of the Thruster car doesn't
break 1.4s. Another problem is the potentially very high initial
acceleration.
* Electrical drive (acceleration, power and traction limited):
0-60mph: 1.78s
* Electrical drive (acceleration and power limited) with air-rocket
downforce sufficient to provide maximum traction.
0-60mph: 0.82.s.
5.0G for 200ms after which at maximum electrical power [*] the
acceleration falls evenly from 5.0G to 1.86G over 0.62s.
To provide the necessary downforce at 5G maximum acceleration and a
coefficient of friction of 1.5 the maximum required downforce is 47kN or
10,400 lbf (enough to accelerate the car by 2.3G) for the first 200ms.
Required downforce then falls reaching zero at 0.82s. Total impulse for
the 0-60 acceleration period is 23.8kNs (a small O motor).
That's equivalent to 34kg or 75lb of air used in rockets exhausting
upwards at a typical air rocket ISp of 700 Ns/kg.
* Electrical drive plus horizontal air-rocket drive (acceleration, power
and traction limited)
0-60mph: 1.12.s.
Using the same 75 lb of air for horizontal acceleration.
* Electrical drive plus swivelling air-rockets (acceleration, power and
traction limited)
0-60mph: 0.71.s.
Using the same 75lb of air, initially to provide downforce then
swivelling to provide linear acceleration, and limiting initial
acceleration to 4G.
Above 60 mph the downforce of the wind should be enough to keep the car
on the road at maximum electrical acceleration.
Plus, if the rockets fire upwards then the pedestrians don't get blown
away. Just deafened :)
However Elon is only talking about 0-60mph in just under 2.0s, so maybe
his rockets don't point upwards - that's about what you get with a tyre
friction coefficient of 1.4 under 1MW electrical power alone.
Peter Fairbrother
[*] Chain rule!
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