What if? ( upgrade package )

[PV4EV]

Thanks for the above post - lots to think about. Personally though I spend very little time at 70mph. Looking at the logs most of my driving is accelerating (hard) from 20 to 60 and braking back down again as I drive through the twisty country lanes locally. Other than that I am usually stuck at 40mph on main roads behind other traffic. Freeway / motorway driving at 70mph makes up a small part of my driving.

With the way I use my car I assume a 20% weight saving would have a much bigger effect on range than the 7% mentioned.

A fairly huge 20% weight reduction would definitely improve all the 20 to 60mph hard acceleration runs !

If you were to theoretically maintain a steady 40mph on a long run the effect on efficiency / Wh/mile would be better due to air resistance being much less of a problem, and would improve it by approx 13% or so. BUT whilst 40mph might be a reasonably average speed on a typical journey in traffic where's there's a much of slowing/accelerating the realistic efficiency gain would be less than that in reality. Changing the speed of something uses a lot more energy that just maintaining a fixed speed.

 

[PV4EV]

Are you sure? I think that air resistance goes up cubically with speed, not exponentially. That's a *big* difference.

If the component part of the air resistance calculation was heavily influenced by the cube of the speed then maintaining 100mph instead of 50mph would require up to 2,500 times more energy !!



There's a very good article summarising the maths with respect to vehicles, here :-

http://wps.aw.com/wps/media/objects/877/898586/topics/topic02.pdf


The air resistance component is approx proportional to the speed squared as follows :-

Fa = 0.5 * ( Cd * Ca * R * Cv^2)

Fa= air resistance force
Cd=Coefficient of Drag
Ca=frontal area
R = rolling resistance (separate equation)
Cv= Speed of vehicle.


R= u * M * G

u = rolling resistance coefficient of the tyres on the surface type typically small number like 0.007 to 0.015
M = Mass of vehicle, Kg
G = constant, force due to gravity, 9.8 meters/second^2


Power needed to maintain a steady speed = (R + Fa) * Cv

There is a Cv^3 term in there, but its effect is closer to Cv^2 due to the size of the constants


The actual energy required is subject to various losses due to electrical resistance, mechanical transmission losses, efficiency of the motor and so on.

 

[PV4EV]

In my text book aerodynamic drag depends on speed to the power of 3. Calling it an exponential increase is not correct, but it gives many folks a familiar concept of "growing not linear, but waaaay steeper".

Edit: appropriate post here: Roadster Efficiency and Range

As per previous post there is a V^3 term in the maths, but at normal road speeds the increase in energy required is closer to V^2.

Referring to the excellent link you provide at Roadster Efficiency and Range shows that doubling the road speed from 50 to 100mph requires approx 4.5 times the BHP, and doubling from 60 to 120mph requires 4.7 times the BHP.

Hence my approximation of energy required increasing exponentially at the sort of road speeds we're discussing !

However, I agree that at supersonic speeds the assumption that its exponential goes right out the window :smile:

The Model S Cd was mentioned by Elon to be 0.225 which would be an excellent value.

Really ? That would be a stunning figure if they can achieve it !

 

[vfx]

He did mention they would not exceed the EV1's cd at all.

 

[Norbert]

According to this blog by Tesla: Roadster Efficiency and Range | Blog | Tesla Motors

In terms of Wh/mile, aerodynamic losses are somewhat, but not exactly, with the square of the speed.

Again, in terms of Wh/miles, tire losses are almost (but not exactly) constant over speed (though, I think, proportional to weight).

Drive train losses also go up with speed, but not as much as aerodynamic losses.

 

[doug]

Besides this being a tangent for a different thread... I need to clear up some basic math and freshman physics here.
Don't confuse energy and power.
E=F*d; P=F*v

So the aero drag force and the energy lost to it go as v squared, but the power goes as v cubed. This is perfectly consistent, yet still not an exponential.

 

[richkae]

I totally understand that lots of people want a 90kWhr battery and 395 mile range.
But I'm kind of shocked that nobody expresses interest in the horsepower upgrade, lots of people spent $20k on the Sport option.

( Yes I want a lighter battery and would love for the Roadster to have a lower Cd, but changing the aerodynamics at this point is extremely hard - that will have to wait for next generation Roadster. )

 

[bolosky]

I was saying that the power of aerodynamic drag goes up cubically in the speed. Since speed itself is linear in speed, then the losses are quadratic.

That is to say, if you were able to isolate the drag component of the power and see what happens on the power gauge of the Roadster, you'd see it go up with speed^3. However, the energy lost to drag/mile only goes up with the square of speed, because, well, you're going faster so you get more miles per second.

Make sense?

 

[doug]

^^ This.

 

[Alan]

I totally understand that lots of people want a 90kWhr battery and 395 mile range.
But I'm kind of shocked that nobody expresses interest in the horsepower upgrade, lots of people spent $20k on the Sport option.

As above, I am more interested in improving performance than range.

The battery pack weighs 450kg (sorry using metric for this), lets assume 100kg is the casing, cooling etc. Thats 350kg of batteries. Earlier in the thread it says that the new batteries could give 90kWh rather than 53kWh. If the new cells were used to keep the capacity the same that would drop the weight of the batteries from 350kg to 200kg.

The car weighs 1235kg so saving 150kg would (just using f=ma and ignoring traction etc) improve acceleration by abut 10% and also improve handling (assume new battery pack would have lower center of gravity as well as less mass) and braking.

You could argue that the $20K sport option, which many have gone for gives about a 5% improvement in acceleration so a new battery pack giving a 10% improvement for the $35K mentioned seems sensible. If it also included an improved PEM for more power then its a bargain.

My point is that the improved cell technology makes two options possible, a performance focused upgrade and a range focused upgrade. A performance focused upgrade should be cheaper than the range based one as less cells are required in the pack.

 

[tennis_trs]

I totally understand that lots of people want a 90kWhr battery and 395 mile range.
But I'm kind of shocked that nobody expresses interest in the horsepower upgrade, lots of people spent $20k on the Sport option.

( Yes I want a lighter battery and would love for the Roadster to have a lower Cd, but changing the aerodynamics at this point is extremely hard - that will have to wait for next generation Roadster. )

As above, I am more interested in improving performance than range.

...

Me too, I very rarely make trips beyond my current range where it doesn't make more sense to instead fly. But I'll floor the accelerator most days.

 

[garry753]

I would be much more interested in the range part of this upgrade than the performance boost. If I could keep the same performance (I own a Sport), and increase range to 390 - 400, it would allow me to reach other Texas cities and return home to Austin on close to one charge.

I would pay something extra if the new upgrade included the capability to do a 45 minute DC quick charge like the Model S as well.

 

[vfx]

We are pretty divided on this!

I feel that the current Roadster acceleration blows everyone away (including me!) so more HP is overkill AFAIC. Would like it yes but as the car is daily driver and I want range. Top speed is pointless to me. If the car only went 90MPH but could do the same 0-to 60 (or better) it would not have dissuaded me from buying one bit.

A split of both would be considered but would have to see the exact numbers and prices.

 

[dsm363]

I agree. More range and maybe use of the new Tesla plug and DC fast charging would be great. 250 miles of real highway driving at 70 mph on a standard charge would be great.

 

[rolosrevenge]

If you kept with the same range but a smaller pack, in addition to better performance you could have ... a bigger trunk!

 

[TEG]

I feel that the current Roadster acceleration blows everyone away (including me!) so more HP is overkill AFAIC...

That coming from someone who doesn't have a sport model, and has been driving a lot of Roadster miles so has had plenty of chance to "get used to it", and become jaded... But no... 0-60 in 4s is still fairly awesome even to those fishing around for bragging rights. It still shocks the passengers and affords you passing opportunities through busy traffic that would not be possible in other cars.

On the other hand, Elon used to drive a McLaren F1... (~3.2s)

 

[jory]

the performance is already more than enough. i would pay for increased range. i wouldn't mind more trunk space.

 

[SByer]

I could do with a bit off the 0-60 time. It'd be nice to get under 4. The 'other car' we have is much better suited for road trips, in spite of the <shudder> gas usage. Susan doesn't exactly travel light, either, so I'm not sure the range would do me much good.

But then, I'd pretty much be stuck getting the premium tires to consistently get that 0-60 time.

But boy, wouldn't it be so cool to be able to tell all the doubters that my car just kept getting better over it's lifetime, including range and quickness.

 

[bolosky]

As above, I am more interested in improving performance than range.

The battery pack weighs 450kg (sorry using metric for this), lets assume 100kg is the casing, cooling etc. Thats 350kg of batteries. Earlier in the thread it says that the new batteries could give 90kWh rather than 53kWh. If the new cells were used to keep the capacity the same that would drop the weight of the batteries from 350kg to 200kg.

The car weighs 1235kg so saving 150kg would (just using f=ma and ignoring traction etc) improve acceleration by abut 10% and also improve handling (assume new battery pack would have lower center of gravity as well as less mass) and braking.

You could argue that the $20K sport option, which many have gone for gives about a 5% improvement in acceleration so a new battery pack giving a 10% improvement for the $35K mentioned seems sensible. If it also included an improved PEM for more power then its a bargain.

My point is that the improved cell technology makes two options possible, a performance focused upgrade and a range focused upgrade. A performance focused upgrade should be cheaper than the range based one as less cells are required in the pack.

The Roadster 0-60 time depends on two things. At low speed, the limit is the amount of torque that the motor can generate (which in turn is related to the amount of current that the PEM puts out). At higher speed, the limit is the amount of power that comes from the ESS. This is why the torque curve looks like it does: flat from 0 to about 40, and then dropping off in a straight line (since power divided by speed is proportional to torque in a fixed gear ratio car). If you were to reduce the cell count, that would in turn reduce the power that the ESS puts out, and it would move the place where the curve transitions to a lower speed. It would also increase acceleration for any given torque, because of reduced mass. Whether the reduced mass overcomes the reduced power depends on the torque, power and mass. It's not at all obvious that a car with fewer cells would actually win at 0-60, and it's pretty clear that it would lose in a quarter mile because most of that time is spent at higher speed where the power limit matters.

That said, it's likely that the higher capacity cells will also be higher power, so what you might actually get with the hypothetical pack is improved performance at higher speeds.

I, for one, would be more interested in improved acceleration at 60MPH that at 30. It's already killer at 30.

 

[bolosky]

Oh, and in answer to Rich's original question: Yup, I'd plop down the $35K in a minute for that. I just wouldn't tell my wife what it cost.