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November 19th, 2017 Total archive posts: 984
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Swapping Motors: A Little Analysis

A few weeks ago I posted some figures on my recently-completed RX7/LS1 hybrid. The car put down 421 horsepower at 6100 RPM and 408 ft-lbs of torque at 4900 RPM measured at the rear wheels on a dynapack. On paper that's a significant gain over my original tuned 13B. I spent about a year fitting a lot of bolt-on equipment to the old rotary including a very rare Knight Sports V-Mount intercooler which I imported myself from Japan. Long story short, with the factory twin sequentials running rich at 12 psi I posted 276 HP@ 7300 RPM and 232 TQ @ 5100 RPM. You can see this dyno plot below:

There are some people who can make up to 300 RWHP with careful tuning on the twins in sequential mode. Beyond that you have to go non-sequential or a single turbo which severely compromises throttle response and spool at under 3500 RPM--in other words during street driving conditions. This was the main reason I went with an LS1 conversion: my car is 90% a street car and throttle response is very important. The original factory sequential twins were good, but the LS1 is much better. Even a small single turbo will take at least half a second to fully respond to throttle input--and sometimes longer. The chart below shows a side-by-side comparison of the two motors. While the dyno plots can't measure throttle response, it's safe to say that under 3500 RPM the LS1 has instant response to throttle tip-in.

The chart shows a clear advantage to the LS1. I make 75 ft-lb more torque at 3000 RPM than my 13B made at its best, and peak torque is up 75%. Torque is transmitted to the ground through the driveline and creates a linear force on the car. As humans, we feel acceleration due to this force which gives us the sensation we use to determine how quickly we are speeding up. So at first blush one would think that the LS1-engined RX7 would accelerate 75% faster than the original 13B configuration.

But the chart above doesn't quite tell the whole story. Notice how the LS1 graph stops at 6500 RPM? (The rev limit is 6800.) Meanwhile, the 13B continues to rev to 8000 RPM. Now, you ask, isn't it unfair to measure the two motors side-by-side when one can rev much higher? If we geared the 13B down relative to the LS1 so that we shifted at the same road speed--in other words, letting each motor hit its rev limit by the end of the gear--wouldn't the 13B have a mechanical advantage over the LS1 that would make the car feel faster?

This is a very important concept that shows why the measurement of horsepower is much more valuable to the enthusiast (or engineer) than torque. Below is a graph where I've corrected the output of the 13B by fitting an imaginary transmission that has an output ratio of 1.23. This allows the 13B to hit its rev limit of 8000 while the output shaft of our transmission spins at 6500.

To calculate force we simply multiply the output of the 13B by 1.23. As you can see, the 13B gains a good bit of torque, peaking at about 286 ft-lbs, a gain of over 50 ft-lbs. But wait a minute...the horsepower is unchanged. Why?

Horsepower is a measurement of torque times the angular velocity of the motor, in this case measured in RPM. (The calculation is actually torque times RPM divided by 5252.) Our imaginary transmission has raised the torque output of the 13B, but it has decreased the angular velocity. In fact, it's decreased that velocity by 1.23--the exact same amount that the torque has increased.

So no matter how we fiddle with the gear ratios of the system, the output torque may change but the horsepower remains the same.

This is why horsepower is such a useful measurement. You can think of it as the maximum performance potential of a given motor regardless of how high it revs. It's a way of comparing a lot of very different types of motors. In this way a 500 HP Viper motor (redline: 6000 RPM) can be compared to a 750 HP Ferreri 248 F1 motor (redline: 19500 RPM). Even though the Viper makes about twice as much peak torque, the F1 motor has greater overall performance. If you put that Ferrari motor in the Viper and geared the transmission appropriately, it would be a much faster car.

Of course, there are other important ways of looking at engine data, such as area under the curves and usable rev range. For instance, study a peaky S2000 or Celica GTS motor and you'll see that much of the torque is generated only at high RPM which give the motors high peak horsepower but not a broad torque curve. It would be nicer if the motor made as much torque throughout the rev range, but that's not possible given the small displacement of those motors. Most race motors are peaky as well, but are geared so that the engine is always spinning at the high end of the rev range.

So what's the point? Well, despite the fact that the LS1 has nearly twice the torque of the 13B (which is what you feel in the car) to say that the LS1 feels twice as fast would be incorrect. In fact, due to the difference in redlines between the two motors, the advantage of the LS1 is only about 43% over the 13B.

Here's why horsepower is useful as a measurement. The torque comparison suggested a 75% difference between the LS1 and the 13B, not 43%. But notice that the horsepower ratio between the two cars was about 52%...much closer to the actual difference between the cars. (The fact that this doesn't work out perfectly is because peak torque and peak horsepower don't usually occur at the same RPM. But generally speaking, the horsepower figure is far more accurate in comparing the performance potential of two dissimilar motor types.)

But just looking at horsepower figures is not enough. You may be able to evaluate the performance envelope of the two motors, but at the end of day it doesn't tell you how quickly the car will move when you hit the loud pedal. In reality, the choices that the car manufacturers make in terms of transmission ratios and wheels affect how the car feels in a big way.

Simply looking at the dyno plot or peak HP/TQ figures in a magazine does not give you enough information to guess how hard a car is going to pull. In fact, even specific power-to-weight measurements (lbs per HP or HP per tonne) are not sufficient. In order to really know, you'll need:

  1. The car's curb weight
  2. The gear ratios and final drive
  3. The diameter of the driven tires (you may have to cross-reference this...look up the size of tire at Tire Rack and then check the specs. Look for the 'Overall Diameter'.)
  4. The peak flywheel torque of the motor

The number you'll be generating is the theoretical acceleration of the car measured in g's (one g being the force applied by gravity to all objects at the earth's surface). Most aggressive street tires can handle a little more than 1g of acceleration before braking loose, and you'll see that most supercar motors generate far more torque than the tires can handle in first gear.

Here's the equation:

acceleration in g's = ( flywheel torque * gear ratio * final drive ) / ( wheel radius * weight )

With torque in ft-lbs, wheel radius in feet, and weight in pounds. Gear and drive ratios are dimensionless.

Let's do some examples, looking only at the first three gears. Most supercars are geared to go 0-60 in two gears and 0-100 in three. Beyond this you are hopefully on a racetrack and not on a public road.

First off, here's my RX7 with the tuned 13B and original transmission:

  • Curb weight of 2800 lbs
  • 1st: 3.48, 2nd: 2.02, 3rd, 1.39, final: 4.10
  • 25.3" tires
  • Peak flywheel torque: 273 ft-lbs
  • Expected acceleration: 1.32 g's in 1st, 0.76 g's in 2nd, and 0.53 g's in third

Now, the RX7/LS1 hybrid:

  • Curb weight of 2850 lbs (a little heavier with the LS1 motor)
  • 1st: 2.66, 2nd: 1.78, 3rd: 1.30, final: 3.73 (GM T-56 transmission)
  • 25.3" tires (same as above)
  • Peak flywheel torque: 480 ft-lbs
  • Expected acceleration: 1.59 g's in 1st, 1.06 g's in 2nd, and 0.77 g's in third

So now the comparison. Gear for gear, the LS1 hybrid pulls harder than the original 13B in the first three gears. While both have the ability to spin the wheels in first gear, the 13B generates 83% of the LS1's acceleration in 1st; only 72% in 2nd; only 68% in third. (Flipped on it's head, that's an advantage to the LS1 of 20%, 39%, and 47% in gears one through three.) If you drove these cars back to back you would walk away with the sensation that the LS1 is significantly quicker and climbs to high speeds much more freely than the 13B. (Some of this is due to the RX7's antiquated 5-speed transmission which suffers from wider spacing between gears.)

Let's pull it all together:

  • We looked at peak torque of the motor and saw at 75% difference. Smokin'!
  • We looked at peak horsepower and saw a 52% difference. Ah, still pretty cool.
  • We scaled our dyno plots and saw a 42% difference in relative torque. Respectable.
  • We analyzed the complete car packages and found a 20-47% difference depending on the gear. Hmm, not what you expected, right?

So the interesting takeaway here is that the big numbers of the LS1 don't look quite as big when you take the whole picture into account. (Note: Your author knew this going in, and did the swap for reasons other than ultimate acceleration.)

What I like about the acceleration measurement is that it describes the performance potential of the car, and how the car will feel when you go full throttle. Many magazines post 1/4-mile times, but numbers here have a lot to do with launch technique, clutch performance, tire quality/pressures, racing surface, temperature, altitude, wind, and so forth. The measurement I'm using assumes ideal conditions and provides, in my opinion, a more objective and fair way to evaluate how the car will feel when you mash the gas pedal.

Here's some comparisons to modern supercars of acceleration in the first three gears. Remember, this is only a view of the peak acceleration and not an exact measurement of performance--but it does capture how fast the car feels to the driver in terms of being pushed back into the seat.

  • The 2006 Corvette Z06 is about 10% down in the first three gears. This is mostly due to the additional 300 lbs that the Z06 carries over the hybrid, as the gearing and motors are almost identical.
  • The Ferrari F40, my second-favorite car of all time, posts a dismal 25-30% loss--the result of a old-school five-speed transmission--although the curb weight figure that I have (2646 lbs) is higher than I remember from the 80's.
  • The vaunted McLaren F1 (first favorite!) is also down 10-15% in the first three gears. This was surprising, but upon inspection you can see that the car was geared for high-speed runs. You can hit 77 MPH in first gear, and the top of third gear is over 145MPH.
  • The Ferrari Enzo is geared low and is up on the hybrid by 15% across the board. In fact, it generates over 1.2 g's in second gear, the highest of this group.
  • The Carrera GT is up 10% in first, but loses about 4% in the next two gears due to wider spacing.
  • The 2007 911 Turbo has the same acceleration in first gear, but it can use a lot more of that 1.6 g's due to its all-wheel drive system. The next two gears are still pretty short, but the portly 3495 lb curb weight starts to take its toll--about 20% down for the next two gears.
  • My 2004 STi is geared ridiculously low. At 80 MPH on the freeway I'm at 3200 RPM. But even so, the STI is over 20% down in the first three gears.
  • I did a bit of searching on rx7club.com to find some other RX7s running around 420 RWHP. Typically this takes a medium-sized (TS04 or T04R) turbo at 16-19 psi, a ported motor, and about $10K worth of other mods. These cars generally make about 320-330 ft-lbs of peak torque, so I've used that figure. A car like this pulls even in first gear but loses 13% in second and 18% in third.
  • 13B's with really big turbos at 20 psi+ hit about 500 RWHP and 400 ft-lbs of torque. In this case, these rocket ships are up 22% in first gear (higher than the Enzo) but fall to parity in second and third gear. However, most single turbo 13B's enjoy their peak torque for only about 1000 RPM; they generally are below 200 ft-lbs until 4000 RPM and the torque falls off quickly after peak. Not to mention that the throttle response, especially during stree driving, is somewhere between bad and horrendous.

Much of the data used in calculations above was taken from websites like Supercars.net which is usually accurate.

You can also see why final drive or 'rear-end' changes are popular. By swaping a different ring and pinion gear set, you can significantly alter your car's acceleration. But you do this at the expense of more frequent shifts, higher RPM at cruising, and lower gas mileage. And in many cases--like the quarter mile--an extra shift may mean a slower overall time. A good example of this is the STi and it's arch-rival, the EVO. The original USDM EVO has a 5-speed box that could hit 60 in two gears. The STi needed three gears. So despite a stronger motor and shorter gearing, the STi usually lost the 0-60 contest. Shifts take around 300-500 miliseconds when done aggressively.

It's also worth noting that the sensation of acceleration or 'pull' has some interesting psychological aspects. For instance, cars that rapidly increase their rate of acceleration can feel very fast when they may in fact be slower than cars that are more on/off in their response. Turbocharged cars generally have this rush of acceleration that comes on in such a way that the driver gets to feel it longer, creating a more intense sensation.

Interestingly, these same turbo cars can suffer from torque fall-off at higher RPM and can feel 'weak' or 'limited'--sometimes referred to as 'running out of breath'--as they go towards redline. These cars can exhibit this behavior because of small compressor and turbine size that are chosen for throttle response and not high-end flow; the same turbos that generate the big burst of speed at lower RPMs actually choke the motor as the revs rise.

But I digress. My point here is that by analyzing the relative performance of the two motors in my RX7 clearly shows that figures like peak horsepower and torque do not tell the whole story.

by Christopher Heiser on September 5 02:54
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