Speculative Aerodynamic Model of Thrusters

[Silent Ludicrosy]

MESM,

A couple more thoughts about your demo:

One of the simpler ways to calculate the force caused by an aerodynamic phenomenon is to calculate the net change in momentum of the air/gas. For example in a rocket engine if you multiply the velocity of the exhaust by the mass flow (assuming perfectly expanded) the result exactly equals the thrust. It’s an extension of newton’s second law, an equal and opposite reaction between the exhaust molecules and the nozzle.

Long story short, there has to be a net change in air velocity upward to create a downward force on the car. If air comes out equally in every horizontal direction, the net force on the car is zero.

In your paper example, the air velocity initially comes out horizontal, but the drooping paper turns the flow downward, which results on an upward force on the paper.

 

[MESM]

@Pmac727 Could I try and convince you otherwise using this video ?

I see where you are coming from but the experiment in the second video does not have the downward flow that you saw in my original demo (It is hard to build a convincing demo with cardboard and a glue gun!). One of the demos has a tube glued to the bottom of my car and I can measure a pressure reduction under the car. My claim is that the Bernouilli effect dominates here (when you increase the kinetic energy you reduce the pressure / potential energy)

@Joerg did a summary at 9:49 AM and suggested that the curtain model might have the same 'pebble risk' as the rocket thruster options. I have only just worked out how to do the calculations. I think I will be able to post saying that the curtain that creates suction only needs to be ~30 cm wide x 20 cm high with ~120 mph air. If I am right there is barely any thrust at all - just suction. I will get back to you.

Thanks MESM

 

[MESM]

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!):

1. What is the velocity of the air in the suction curtain (this is the model that I prefer)
2. 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)
3. 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:

• @Partick0101 https://teslamotorsclub.com/blog/2018/06/29/tesla-roadster-rocket-thrusters-explained-by-tesla-patent/
• and ‘Tesla Roadster Rocket Thrusters Explained By Tesla Patent’ https://teslamotorsclub.com/tmc/threads/tesla-roadster-rocket-thrusters-explained-by-tesla-patent.121313/

 

[buttershrimp]

I could go into a long explanation and critique of your theory and get @jimmy_d or @lunitiks on all y’all but I shall give you a more elegant demonstration of the top secret technology in the wild...

 

[Joerg]

@MESM amazing insights, yes speculation, just as much as jimmy or lunitiks do, I like it!
@buttershrimp you forgot to mention our expert bladder.
COPV filled with water, why not?;-)

 

[BioSehnsucht]

To solve the problem of air being hot enough to melt the COPV or too cold to expand usefully for thrust - why not only cool the air enough to not melt the COPV - or better to not cause undue discomfort to the occupants? It seems unlikely the design would call for a compressor sized to refill the tank fast enough to melt the tank anyways. But similarly the power to chill it completely down to maximum compression seems unlikely as well. Plus, it's not like it's a vacuum sealed container that will hold the temperature difference, it will radiate / etc the heat to some extent. It's fine if it's perhaps got a surface temp in the range of 90-100 degrees or so but the higher the surface temp ends up the more annoyed the driver is going to be to have this hot radiating thing right behind them, AC or no. Just because some supercars have hot radiating engines right behind the driver doesn't mean a Tesla driver would appreciate this. So I would think either a slow enough compression refill that the natural radiation/convection/etc is enough to keep temperatures under control without cooking the driver, or that combined with a small heat exchanger connected to the battery or motor coolant loop.

As for thrusters arranged to thrust up, or sideways, or suction inducing sideways, another possibility is a combination. Instead of focusing on the SuperDracos, look instead to the thruster clusters of the Dracos. Then you could perhaps use it in multiple ways.

Of course not so many in a cluster probably, as you quickly would go past the "~10" comment from Musk.

 

[Brando]

surface area of Model 3 is about

180" x 65" = ~ 11,700 square inches

If we could decrease the air pressure under the car by 2% (of 14.6 lbs./sq.in.) = ~ 0.25 lbs./sq.in. pressure differential

0.25 lbs./sq.in. x 11,700 sq.in. = 2925 lbs. of down force

interesting - can air jets reduce the air pressure under the car ?? I don't know.
Can't wait.

 

[MESM]

@BioSehnsucht thank you for your comment – I loved the Draco rockets. They should have played some music.

I am not so sure about any kind of temperature change to the COPV gasses unless it happens slowly. I find it hard to think of fast heating of the air as it is released – my Uncle worked on a project where they stored energy in compressed air but when they expanded it they burnt gas in the expanding air to keep it at room temperature (obviously no burning anything in a Tesla!).

On the SpaceX rockets they use cold nitrogen thrusters.

I don’t think that there is a problem with compressing the air – they can do that slowly and use a small radiator to cool the gas as it is compressed.

I think that you are right that he can use computer modelling to study all the options (up-sideways-and-suction) but I think that one of those processes will dominate! (Let’s see if my guess is right!)

@Brando Thank you for your comment. I can’t wait either!

 

[Ben W]

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 believe the maximum exhaust velocity is limited by the speed of sound of the compressed air. An exhaust velocity of 1500mph would require the air to be heated to about 1000 °C, well beyond the melting point of aluminum (660 °C), so I don't think that's possible in the Roadster scenario..

For air compressed to 5500psi at room temperature, cutting a 0.75-square-inch hole (~5 cm^2) in bottom of the COPV would be sufficient for the car to temporarily levitate, with an exhaust velocity of roughly 340 m/s (760 mph). The air in the COPV would initially deplete at a rate of about 80kg/s, so with a 54kg COPV the hover could be sustained for about half a second if the aperture were made variable. (Check my math.)

If the COPV size were increased to 0.9m diameter, and two of them were used, then the compressed air mass would become 365kg, and a hover of 4+ seconds would become possible. Turbo Boost anyone?

 

[AWDtsla]

If the COPV size were increased to 0.9m diameter, and two of them were used, then the compressed air mass would become 365kg, and a hover of 4+ seconds would become possible. Turbo Boost anyone?

That's a huge handling penalty. It would seem to me that you would have to use this system excessively while on the track, and I imagine at not good efficiency considering the amount of power lost to heat. Also given a limitation of the flow rate of the compressor, I believe the duty cycle would have to be quite low, you couldn't actually use it to compensate for the handling penalty in every turn. I can't see how this system can be used for more than the dragstrip.

 

[Ben W]

That's a huge handling penalty. It would seem to me that you would have to use this system excessively while on the track, and I imagine at not good efficiency considering the amount of power lost to heat. Also given a limitation of the flow rate of the compressor, I believe the duty cycle would have to be quite low, you couldn't actually use it to compensate for the handling penalty in every turn. I can't see how this system can be used for more than the dragstrip.

Agreed that a 365kg set of tanks is completely over the top. A single 100kg tank, if emptied downward in a single burst, would be sufficient for a nearly 15-meter "vertical leap", more than enough for KITT-simulation purposes. (Math: 100kg of air directed downward at 340m/s would cause a 2000kg car to recoil upward at 17m/s, reaching a maximum height of ~14.5 meters.)

By the same token, 365kg of air blown downward at 340m/s, could propel a 2000kg car upward at 62 m/s (139MPH). The car would reach a maximum height of 192 meters during this jump, before it came smashing down on the concrete. This doesn't sound like a good idea, even for Elon.

 

[Silent Ludicrosy]

I believe the maximum exhaust velocity is limited by the speed of sound of the compressed air. An exhaust velocity of 1500mph would require the air to be heated to about 1000 °C, well beyond the melting point of aluminum (660 °C), so I don't think that's possible in the Roadster scenario..

The exhaust velocity is not limited by the speed of sound. Air traveling at Mach 1.0 that passes through a diverging nozzle will accelerate faster than the speed of sound. How much faster depends on the pressure ratio at the source and the exit.

Elon Musk states on his Joe Rogan interview that the air is compressed to around 10000 psi. If the air is released through an optimized converging/diverging nozzle, the static/total pressure ratio is .00147 at sea level which on the table correlates to Mach 5+. Assuming the air temp in the COPV is limited to around 1000*F for metal temp limits, the max velocity of the exhaust would be around 2500mph. That correlates to an optimum nozzle exit/throat area ratio of 30:1. By using a nozzle with greater than 30:1 geometry, Tesla could overexpand the flow which would put shockwaves at the nozzle exit that slow the flow before it goes out into the atmosphere/peoples faces.

 

[Ben W]

The exhaust velocity is not limited by the speed of sound. Air traveling at Mach 1.0 that passes through a diverging nozzle will accelerate faster than the speed of sound. How much faster depends on the pressure ratio at the source and the exit.

Elon Musk states on his Joe Rogan interview that the air is compressed to around 10000 psi. If the air is released through an optimized converging/diverging nozzle, the static/total pressure ratio is .00147 at sea level which on the table correlates to Mach 5+. Assuming the air temp in the COPV is limited to around 1000*F for metal temp limits, the max velocity of the exhaust would be around 2500mph. That correlates to an optimum nozzle exit/throat area ratio of 30:1. By using a nozzle with greater than 30:1 geometry, Tesla could overexpand the flow which would put shockwaves at the nozzle exit that slow the flow before it goes out into the atmosphere/peoples faces.

I had assumed the air in the COPV would be closer to room temperature, since there may be diminishing or negative returns for actively heating it: at 600 °C the COPV could hold only one-third the air mass (at max pressure) that it could at 25 °C, which more than negates the increased exhaust velocity, in terms of total thrust for a given volume COPV. True that supersonic flow can be achieved with a properly designed nozzle, but the max speed is still proportional to (a low multiple of) the speed of sound. The highest specific impulse ever achieved in practice for a nitrogen cold-gas thruster is 73 seconds, implying an exit speed of about Mach 2.

 

[AWDtsla]

I had assumed the air in the COPV would be closer to room temperature, since there may be diminishing or negative returns for actively heating it: at 600 °C the COPV could hold only one-third the air mass (at max pressure) that it could at 25 °C, which more than negates the increased exhaust velocity, in terms of total thrust for a given volume COPV. True that supersonic flow can be achieved with a properly designed nozzle, but the max speed is still proportional to (a low multiple of) the speed of sound. The highest specific impulse ever achieved in practice for a nitrogen cold-gas thruster is 73 seconds, implying an exit speed of about Mach 2.

COPV that can handle 600C??? Is there no resin in the carbon wrap? I'd imagine even without active heating the tank would have to be thermally managed, especially to prevent repeated deep thermal cycles just from the compression and release of air.

 

[Silent Ludicrosy]

Compressing the air to 10000 psi would result in temps well over 1000F, so there wouldn't be any sort of heater needed for the COPV. The equation I'm using is T2 = T1 (P2/P1)^(.4 / 1.4).

1000*F is a high extreme using aluminum limits, because I don't know what the actual COPV limits are. I imagine the air will actually be something less than 600C but above room temp. Otherwise it would need a big heat exchanger between the compressor and COPV. Hopefully Tesla will do something with the excess heat, like cycle it back to a cold battery or cold interior.

One other thing about temps. If you have room temperature air at 10000 psi and expand it to 14.7 psi through a diverging nozzle, you'll see extremely cold temps. Like frostbite danger, ice buildup potential. If the air is hotter in the tank, those problems are less of an issue.

 

[Ben W]

Compressing the air to 10000 psi would result in temps well over 1000F, so there wouldn't be any sort of heater needed for the COPV. The equation I'm using is T2 = T1 (P2/P1)^(.4 / 1.4).

1000*F is a high extreme using aluminum limits, because I don't know what the actual COPV limits are. I imagine the air will actually be something less than 600C but above room temp. Otherwise it would need a big heat exchanger between the compressor and COPV. Hopefully Tesla will do something with the excess heat, like cycle it back to a cold battery or cold interior.

One other thing about temps. If you have room temperature air at 10000 psi and expand it to 14.7 psi through a diverging nozzle, you'll see extremely cold temps. Like frostbite danger, ice buildup potential. If the air is hotter in the tank, those problems are less of an issue.

The high temperatures from compression are only transient; the heat will passively bleed off somewhere, or more likely be actively cooled. Assuming the COPV starts off full at room temperature, as the thrusters are used (and pressure drops), the temperature in the COPV will drop as well, which partially offsets the heat added by refilling it. But let's say the COPV can hold 35kg of air at 600C. The specific heat of air at constant volume is about 0.72 kJ / kg * K, so the energy contained by that air (relative to the same air mass at room temperature at the same volume) is only about 14500 kJ, or about 4kWh. The Tesla cooling systems ought to be able to take care of this much heat; it's about equivalent to the waste heat generated by a half-charge of the battery.

On the flip side, if the COPV is held at room temperature, the expanding air will be very cold, yes. But only a small part of that cold temperature will be transferred to the nozzle (pedantically, heat from the nozzle lost to the air stream), which can be counteracted by actively heating the nozzle. But in the end, much less energy would be required to keep the nozzle warm than would be required to heat all the exhaust air back to room temperature, say. (Or equivalently, to heat the COPV air to 600C so that it is room-temperature on exit.)

 

[MESM]

Elon’s latest tweets seem to favour this version of the Roadster 2020 SpaceX options:

(a) 2 thrusters on each side of the car

(b) 2 front and back

(c) 2 under the car

(that gives us the ten promised thrusters)

Given his latest comments it now seems to be that the thrusters on the front and the side of the car would have to just chuck-momentum-out to change the momentum of the car. The two thrusters under the car would create a pressure effect; IF the car can actually hover then the horizontal thrusters must be (slightly) aimed above or below the horizontal (or the car would roll around the axis of the two downward facing thrusters – it is not stable in a hover with only two thrusters underneath)

The thrusters at the rear might also enhance the diffuser’s suction effect but Elon has now said that the car would operate near the limit of human endurance so again most of the effect must come from chucking momentum out the back.

This is not confirmed but it is not good for my favourite theory. I had thought that he would use the Bernoulli effect so that the tyres would provide most of the accelerating forces (a curtain of air at 400 mph) but it looks like most of the accelerating forces are coming from jets of near-horizontal cold gas.

If the forces are not being transmitted to the road via the rubber, then there will be large forces acting in the air around the car that cannot be avoided – in fact those forces will be very large forces because the car probably weights about two tonnes. This is going to be great on the racetrack so long as there are no light cars next to you on a corner, but it is getting harder to imagine this in more public spaces!

It would look very impressive though. The COPVs have resin-coatings and so they can’t be kept at high temperatures and the energy need to warm the exhaust air (say 80 kg of air per second) would be modest in total but it seems rather too much to kick out in a second or so. So, it would be impressive because there would be a cold white plume from each thruster.

When I guessed the COPV capacity I used the pictures of the Dragon capsule to estimate their volume (see my earlier pixel counting) but my assumption that Elon would reuse the Dragon’s pre-certified COPV spheres is probably wrong since he seems to do everything from first principles! The total mass of compressed air may be much bigger than we thought because Elon has said that (1) you get three uses of the COPV per full compressed air charge and (2) the car works at the limit of human endurance. The argument that the high mass reduces the cars performance does not work because with the air onboard you can have any performance that you want and without the air you still get stunning performance (but *just* battery performance!).

Finally imagine an electric car doing 250 mph and THEN you turn on the thrusters …

So sadly, I may soon have to concede defeat for my Bernoulli theory – but not yet!

 

[MESM]

By the way - thank you to everyone who contributed to this forum. It has been great fun.

I predict that Elon will reveal some of this stuff before the end of March because Tesla would like to have a better share price when some of their debts mature; if the share price is high then the debts become shares not cash.

 

[MESM]

Ah - we might see a Roadster with the SpaceX option tonight so here are the results of the calculations using everyone's best guesses about the mechanics inserted into my model (These are for my Bernoulli theory).

For the velocity of air in the curtain I am predicting 130 mph (though that will be higher if his curtain perimeter is smaller because he would need more suction). If he reuses the Dragon COPV (which may have just been certified for human rated cabins) then I think that the mass of air in one COPV is ~99.9 kg. Finally pebbles that are thrown up from the curtain should get to about 10 mph.

The predicted acceleration time is about 1.6 seconds to 60 mph.

The problem with Elon is that he does so many things that you never know what he might announce ...

 

[googlepeakoil]

As I understand it the car has up to 10 cold gas thrusters (just pressurised air).
When the batteries are not moving the car the electric enerrgy can be used to pressurise the cylinder (to 5000 atmospheres - a scary amount). This would only be done in "track mode" and for "launches".
I can imagine 4 vents near each wheel / jacking point. These are the ones that could give "lift" to the car - make it literally jump in the air. I'd anticipate you need 5000N per nozzle - 500kg to lift a 2ton car.
2 on the front for braking (would also work to push the car away from an iminent impact by creating a dense air wall). 2 on the rear for 0-60 in <1.5 seconds (combined with the wheel driven power to reduce 0-60 by 0.5 seconds). Maybe 2 on the front or sides that could improve braking and cornering. These last ones could even be up-firing to increase down-force and allow for better cornering that way.
I'd imagine the force blowing backwards would be enormous, 5000 - 10,000NM (500-1000kg of "push"). I think that would be enough to shave 0.5 off the 0-60. I'd imagine a few kWh of energy released within a few seconds. The cannister would probably only be able to run for 20 seconds at full output - it would drain very quickly - but be constantly topped up by the pump in "track mode".
The 500kg blast of air would be pneumatic drill - small jet aircraft loud, 110-120dB, be able to knock people flying backwards 5-10m, and potentially kill - so no way it would be "street legal". I'd imagine cameras and proximity censors would be used to detect nothing "living" was nearby or it would not enable.
Any thoughts?