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Is There a Way to Measure Relative Torque on the Car?

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A chassis dyno can measure it the shop. But that is more or less a one shot deal with the conditions that are in the shop at the time with that specific fuel, weather, etc.

For tuning, is an exact measurement needed or is it adequate to just measure the torque curve between adjustments? If so, is there a device that can be mounted on the engine or transmission that would provide that reference measurement proportional to the torque generated?

Take a look at this : http://www.dynomet.dk/en_portableroaddyno.htm

I'm not sure why he chose that apparatus rather than just use the wheel speed sensors or even the crank sensor. That is clearly a relative measurement since the car's aero, weight, and rotational inertia nor elevation changes in the road could not be estimated accurately enough for an absolute measurement. Even relative measurements could be difficult.

If just measuring acceleration, those sensors and/or an accurate accelerometer could do the trick.

I was thinking something related to the rotational movement of the engine around the crank we be the most accurate and independent of the vehicle's mass, aerodynamics, or changes in road elevation.

I'm quite fond of a program called virtual dyno:

https://barnhill.bitbucket.io/

Funny story, I tested it one time at the drags, tried to make my runs as consistent as possible to minimize any variables.

So same gear, started accellerating at same starting speed and same part of track, etc etc...

But my changes in ignition timing werent registering any changes to the results, so I gave up.

I decided that if it cant register those changes in these near-perfect conditions, it's just not good enough.

Then I went to a dyno, and found that the same ignition timing changes that I made previously, made the same negligable difference. ha!

Results from virtual dyno logging at 100hz, and then with some smoothing applied works quite nicely.

Strain gauging the driveshaft(s) can get you measurements of applied torque; http://www.kasensors.com/en/products/drive-shaft-torque-transducer

To answer your question; for tuning, relative measurements are what you're after. When you start hunting for as much power as you can get, looking at each run relative to the last is what you'll be doing, not necessarily the actual peak numbers.

That would seem to be the way to go. Wireless is the key. I haven't gotten the price on the KA Sensors DSTS, but their stuff isn't inexpensive.

It looks like Caleb at Izzy Racing also has something in that vein:

On-Vehicle Dynamometer, Wireless Strain Gauge / Torque Transducer - Izze... https://youtu.be/jPsKwfQU4KQ

Why isn't this more widely used?

I'd say its down to cost as you've mentioned, plus using it for tuning will still be a little problematic as there are many other environmental factors out on the road which will require many, many runs to average out.

This is why dyno tuning is great for the bulk of the job, it eliminates many of these factors and you can focus in on how your changes are effecting engine torque. The caveat it that a dyno tune should always be checked on the road, as road manners and drive-ability are more important than peak numbers I reckon.