Rx400h Torque & Horsepower Curves

[mindmachine]

Dyno predict

By working backward from reported data we can use physics to predict what torque and horsepower to expect on the dyno (provided the 400h will perform on a dyno).

conversions courtesy of convert.exe from http://joshmadison.com/software/convert/

Given==

Given Quantities in metric [uS] units:

mass (m) = 1980 kg [4365 lbs]

0-60 time (t) = 7.3 s

speed (v) = 26.8 m/s [60 mph]

tire radius (d) = .356 m [14 in]

Reference values in metric [uS] units:

ref system power = 200 kW [268 hp]

ref ICE torque = 288 Nm [212 ft-lbs]

ref Fwd torque = 333 Nm [246 ft-lbs]

ref Rear torque = 130 Nm [96 ft-lbs]

ref Total torque = 751 Nm [554 ft-lbs]

Physics==

Impulse (J)

J = mv = Ft [eq 1]

where F is the force exerted by the road to propel the 400h

Torque (T)

T = Fd [eq 2]

where d is the distance between the road and the drive shaft of the wheel (tire radius)

Power (P)

P = Fv [eq 3]

Torque Solution==

Solving [1] for F and substituting into [2] leads to the following relation in terms of T

T = mvd/t [eq 4]

T = (1980 kg) (26.8 m/s) (.356 m) / (7.3 s) = 2588 Nm acting thru all 4 wheels

The simple breakdown per wheel is 647 Nm [477 ft-lbs] ea, but due to the greater power to the front wheels the breakdown would more accurately be determined by the following...

Using ref torque values to determine breakdown ratios (ignoring gear ratios)

Ratio Fwd: Front Torque / Total Torque ==> (288 + 333) / 751 = .83

Ratio Rear: Rear Torque / Total Torque ==> 130 / 751 = .17

Apply ratios for front/rear torque distribution to each wheel

2588 (.83)/2 = 1074 Nm [792 ft-lbs] per Front wheel*

2588 (.17)/2 = 220 Nm [162 ft-lbs] per Rear wheel

*This Fwd wheel value highlights the need for very strong rims on the 400h (that is a lot of torque).

Power Solution==

Solving [1] for F again and substituting into [3] leads to the following relation in terms of P

P = mv^2/t [eq 5]

P = (1980 kg) (26.8 m/s)^2 / (7.3 s) = 194,810 Nm/s or Watts moving the 400h mass

Thus 195 kW [261 hp] compares well with the advertised 200 kW [268 hp] reference value.

Apply ratios for front/rear to power distribution

195 (.83) = 162 kW [217 hp] at the Front axel

195 (.17) = 33 kW [44 hp] at the Rear axel

Conclusions==

Clearly the 400h is forward bias in the power delivered to the ground.

It will be interesting to see if these numbers play out if/when someone actually gets the 400h to perform on a dyno.

Fun with numbers==

So what would the 400h be like if we could put one of the hefty fwd electric motors into the rear of the car?

Using ref torque values to determine breakdown ratio

Ratio Fwd Electric: Front Elec Torque / Total Fwd Torque ==> 333 / ( 288 + 333) = .54

Apply ratio for front elec torque distribution to each wheel

1074 (.54) = 580 Nm [428 ft-lbs] per Rear wheel

Now, summing up the new torque from all 4 wheels

2(1074) + 2(580) = 3308 Nm acting thru all 4 wheels

Solving [4] for t

t = mvd/T [eq 6]

t = (1980 kg) (26.8 m/s) (.356 m) / (3308 Nm) = 5.7 s from 0-60 mph mph)

I will leave it to the reader to show that this translates to a 1/4 mi time of 13 s with a top speed of 141 mph (assuming the Lexus 112 mph speed limit feature is defeated).

Yes nice work and I agree with the calculations from an engineering standpoint, but!!!!!! Your calculations say what is possible in theory.

It still comes down to the programming of the synergy drive system as to how much torque is allowed to be applied to the wheels at any time based on the formulas used by the Toyota engineers. The programming of the computer power allocation synergy drive system is still an unknown.

Oh and yes i agree, this is why you need to be careful about buying any after market wheels for the car, as for me I will use nothing but OEM wheels designed for the 400h. Your calculations confirm the tire wear issues are due to an over abundance of torque and if you have a heavy foot you are going to pay in tire wear.

[skyfish400h]

Yes nice work and I agree with the calculations from an engineering standpoint, but!!!!!! Your calculations say what is possible in theory.

It still comes down to the programming of the synergy drive system as to how much torque is allowed to be applied to the wheels at any time based on the formulas used by the Toyota engineers. The programming of the computer power allocation synergy drive system is still an unknown.

You are correct that when it comes down to the torque value at each wheel, I had to take some liberties to smooth over the unknowns about how the power is distribututed front to back.

However, the total force value needed to move the car from 0-60 in 7.3s is not thoretical. This is an observable fact in the world, and can be verified. The physics assume constant acceleration, which is a safe assumption, since the way you feel being pushed back in the seat, feels pretty much the same thru that speed range.

Oh, and I'm not retired (yet). I just needed to bone up on these kinds of calcs for work, and I figured this was a good outlet.

[jkatsoudas]

So what would the 400h be like if we could put one of the hefty fwd electric motors into the rear of the car?

I will leave it to the reader to show that this translates to a 1/4 mi time of 13 s with a top speed of 141 mph (assuming the Lexus 112 mph speed limit feature is defeated).

Ahhhh, I sense an aftermarket opportunity. "Retrofit kit w/ larger rear electric motor new computer chip turns RX400h into a Porsche Killer!" Can it also please defeat the "I agree" screen? :whistles:

[Jim Clark]

So what would the 400h be like if we could put one of the hefty fwd electric motors into the rear of the car?

I will leave it to the reader to show that this translates to a 1/4 mi time of 13 s with a top speed of 141 mph (assuming the Lexus 112 mph speed limit feature is defeated).

Ahhhh, I sense an aftermarket opportunity. "Retrofit kit w/ larger rear electric motor new computer chip turns RX400h into a Porsche Killer!" Can it also please defeat the "I agree" screen? :whistles:

No "I Agree" screen on our '08 400, warning screen comes up briefly and disappears.

I'm still not buying 550+ ft lbs of torque for our cars (at the wheels). Are you all in some sort of fantasy world? I want to see credible dyno #'s. Unfortunately, our cars will probably shut down if exposed to a 4-wheel dyno so we'll never really know.

[JimsGX]

So what would the 400h be like if we could put one of the hefty fwd electric motors into the rear of the car?

I will leave it to the reader to show that this translates to a 1/4 mi time of 13 s with a top speed of 141 mph (assuming the Lexus 112 mph speed limit feature is defeated).

Ahhhh, I sense an aftermarket opportunity. "Retrofit kit w/ larger rear electric motor new computer chip turns RX400h into a Porsche Killer!" Can it also please defeat the "I agree" screen?:whistles:

No "I Agree" screen on our '08 400, warning screen comes up briefly and disappears.

I'm still not buying 550+ ft lbs of torque for our cars (at the wheels). Are you all in some sort of fantasy world? I want to see credible dyno #'s. Unfortunately, our cars will probably shut down if exposed to a 4-wheel dyno so we'll never really know.

From Road & Track:

So one might ask, "How powerful is it?" and Lexus would tell you that the total system power is 268 bhp, with 208 of that produced by the V-6. But torque is another thing altogether, as the electric motors generate their peak twisting force at revs far lower than the gas engine's 4400 rpm…try 247 lb.-ft. at 0-1500 rpm for the front motor, and 96 lb.-ft. at 0-610 rpm for the rear. So there's no single, tidy torque figure here that's in any way relatable to non-hybrids. Instead, Lexus offers this interesting nugget — total axle torque at launch (that is, after torque multiplication through gearing) is 3500 lb.-ft. Yeouch!

And another pertinent comment I googled concerning the 3500ft lbs.:

Torque inceases with every gear reduction. If the differential ratio is 4:1 and low gear is 2.5:1 then the torque at the wheel would be 10 times the engine torque. Since the wheel speed would be 1/10 engine speed the HP at the wheel would equal engine HP minus friction losses in the drivetrain.