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Bad Inspiration

Appendix J

Jay Chen
Mar 1, 2007

I got a two-sentence e-mail from someone who clearly wasn't aware what he was asking for:

How does a rally car only have 300hp but also have 406lb-ft of torque? What can I do to create that much torque in my car?

Naturally, there's an obvious, simple answer, and a complicated one. As usual, I completely overlooked the simple answer and got myself all confused and intrigued trying to figure out the complicated version.

But the simple answer goes like this: per FIA rules, WRC-class rally cars must run a restrictor plate with a 37mm orifice in front of the turbo compressor housing on 2.0-liter homologation engines. The size of the orifice basically limits the rate of airflow into the engine. Since the internal combustion engine is basically a complicated air pump, this flow limitation caps the total engine output. Making the best of their situation, rally engineers use quick-spooling turbos to reach the limit of that restriction as early, and as long as possible through the rev range. When combined with ludicrous compression, variable valve timing, water injection, and an extremely high level of tuning, their race cars maximize torque from this limited power. According to an ex-Mitsubishi WRC engineer, the key to so much low-end torque is aggressive ignition tuning made possible through better piston and head design and knock control.

Although displacement is limited, the FIA makes no restrictions on changing stroke and limits engines to be bored out within a certain tolerance. Mitsubishi's WRC Evos were bored out to 85.5mm and de-stroked to 86.9mm for less stress at continued high-rev operation, compared to the stock 4G63's 85.0 x 88.0mm bore and stroke.

Assuming you don't want to run a restrictor plate, the secret to big torque is to shift your powerband lower with different cams and cam timing, run a small turbo that moves less air, but spools faster, then advance the timing as far as your hardware will let you. WRC engines will inevitably make more torque because all the parts have been massaged to have a much higher knock threshold.

That said, what really piqued my curiosity is not only how rally engineers are able to build and tune horsepower-restricted engines, but also the profile of the power curve that generates such massive torque down low. One is dependent on the other, because torque and horsepower are mathematical functions of each other.

This unfortunately throws us into the realm of numbers and equations. In the case of a rotating machine like an engine, torque is equivalent to work (force applied over a given circular distance of a constant radius). Similar to how speed is distance divided by time, horsepower is simply torque divided by time. If you divide the distance of your morning commute by the time it takes to get there, it only gets you an average speed. Obviously we don't care about average horsepower from idle to redline. So instead of dividing by however many seconds it takes to rev through the powerband, you have to get fancy and essentially take a derivative of the work done at a given instant. The derivation is easier to show in equation form, but I doubt you care how it's done. You end up with the equation every gearhead should memorize that shows how torque or work is related to power, the rate of work:

Fifty-two fifty-two turns out to be a number worth remembering. It's the factor that converts rotational work in units of lb-ft/minute into units of horsepower. It's also the rpm point that horsepower and torque have to be equal to each other. Just plug in 5252 where you see rpm in either equation and you get power equal to torque or vice versa. This is what we always look for to ensure a dyno run is legitimate, since the two curves have to cross at 5252rpm and horsepower will always exceed torque past this point. This is why we like cars that rev.

Knowing this relationship, you can jump on the computer and make a simple interactive chart and graph of what a theoretical engine's power curve looks like if it made 406lb-ft of torque all the time. It looks like a straight, diagonal line. Or conversely, what the torque curve looks like if somehow you could make 300hp from 2000rpm to redline.

Knowing this relationship allows us to guess what a rally car's power curve looks like. While it's hard to find a dyno chart of a WRC car, it's simple enough to find online that, for a WRC-prepped 4G63, peak power comes at 5500rpm while 406lb-ft of peak torque comes in at 3500rpm. Run this through the equation and you find the car will make 270hp at peak torque. For safety's sake, we'll assume the limiter is set at 6500rpm so you can rev past peak power and land back just below peak power when you upshift.

Since 6500rpm is past peak power, we'll make an arbitrary assumption that the engine is down to 280hp. The number here doesn't affect either curve much, since it's already past the crossover point. Now we have three points on the power curve. To smooth it out, I add another arbitrary point at 2000rpm. Most cars will be lucky to make 70hp at this speed, but since it's WRC we're talking about, let's say they found a way to make a huge amount of power at low rpm. Playing around with the values, you realize that power at 2000rpm really can't be more than 150hp otherwise the torque at that rpm will exceed the peak torque value and look more like an engine making 300hp everywhere. So here's what a rally car dyno curve might look like.

Now here's where the two parts come together. Torque is about instantaneous cylinder-filling or volumetric efficiency. The more air you can cram into a cylinder, the more combustion pressure you can exert on the piston, which results in a larger force shoving the crank down and around, generating torque at the crank. This is useful when you're sliding around in the dirt and trying to keep the engine from bogging down. Horsepower, on the other hand, is a measure of an engine's maximum breathing ability. Which in the case of WRC cars, is restricted by a plate. Try taking quick deep breaths through a straw and you'll understand.

WRC engineers are tricky guys. I didn't realize this until I stared at the charts for while. Their engines are tuned to make peak power just past the 5252rpm point where torque drops below power. By putting peak power so close to the crossover point, you don't stray far from the majority of your torque band before you have to shift. If we go back and change our dyno chart and put peak power at 6500rpm, not only does the power curve drop slightly, torque has dropped significantly by the time you shift.

So why do manufacturers such as Honda build cars like the S2000 that rev almost 4000rpm past the crossover point? Because production engines don't run restrictor plates. This means the engines are displacement limited and not flow limited so they can take advantage of greater volumetric efficiencies that higher engine speeds offer. These cars have nearly flat torque curves and horsepower keeps climbing in a diagonal line, like the example in the first graph.

Jay Chen
Engineering Editor

By Jay Chen
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