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## Measuring power curves without a dyno

### by Julian Edgar

Click on pics to view larger images

Dynamometers measure torque and engine (or wheel) speed, and from this, calculate power. But in the real world, very often dynos are used to see changes in power. For example, when tuning programmable engine management, the dyno operator will do power runs to see if the engine is responding to the tuning changes by developing increased power.

So what if you want to see changes in power – but you don’t have a dyno?

It sounds incredible, but by doing some simple measurements and a few equally simple calculations, you can quite accurately see changes in engine power. You won’t be able to measure the magnitude of the power (that is, how many horsepower or kilowatts you have) but you will be able to see the shape of the power curve, and see relative changes in that power.

And a further point – you’ll also need an empty road, a cheap instrument and a helpful assistant.

### Starting points

 This story is a development of the techniques described at Measuring Real World Engine Performance

Let’s first take a step backwards and show where we’re coming from.

When a car travels down a road, its tyres are pushing back on the pavement. If the push backwards equals the forces the car needs to overcome (on a flat road that’s aerodynamic drag and rolling resistance), then the car will move at a constant speed. If the force pushing backwards (called the tractive effort) is greater than the forces that need to be overcome, the car will accelerate. The greater the surplus of tractive effort, the greater the acceleration.

If the greater the acceleration, the greater the tractive effort; and the greater the tractive effort, the greater the torque being produced by the engine, then by measuring actual on-road acceleration we can see the shape of the engine’s effective torque curve. Taking this approach then automatically takes into account losses that occur at different rpm and gear-train loadings, aerodynamic loadings, losses due to accelerating rotational mass – the whole lot.

### The Instrument

So how do you measure instantaneous acceleration? Performance measuring accelerometers are available in two types - electronic and mechanical.

Electronic accelerometers are most easily achieved by using a ‘g-force’ application in a smart phone. All you need is one that shows actual g-force in big numbers on the screen as it occurs real time.

An alternative is a mechanical accelerometer that uses a tube shaped in a semi-circle in which a small ball bearing moves. Boat and yatching supply companies sell clinometers of this sort – they’re designed to measure the angle of boat heel. However, because they’re designed to measure heel angles rather than acceleration, the scales are calibrated in degrees rather than g units.

So how does this type of accelerometer work?

When the car accelerates, the ball climbs up one arm of the curved tube, showing how hard the car is accelerating. To convert the degrees reading of the clinometer to g readings, simply use a scientific calculator to find the tangent ("tan") of the number of degrees indicated. This means that if the car is accelerating hard enough to move the ball to the 20 degree marking, the acceleration is about 0.36g (tan 20 = 0.3639).

### Testing procedure

So how do you go about the test procedure?

A gear is selected and the car driven at as low a speed as is possible in that gear. After warning your assistant that you are about to start the run, quickly push the accelerator to the floor. Every 1000 rpm (or on low revving engines, every 500 rpm) yell "now!". Each time you yell, your assistant records the accelerometer reading.

In many cars, the acceleration will be too quick for the assistant to keep up, so on the first run do for example 2000, 4000 and 6000 rpm, and in the second run do 3000, 5000 and 7000 rpm.

### Example

So how does all this look? About 15 years ago, I modified a 5-cylinder turbo Audi S4. I designed and made a new boost control and assessed the performance gains by directly measuring on-road acceleration. Here’s the result.

The measured acceleration before and after the fitting of the new boost control shows clearly how much harder the car came on boost. At 4000 rpm, the acceleration in second gear was increased by massive 17 per cent, showing an enormous lift in mid-range torque. Amazingly, this was with identical before/after maximum boost - the boost wasn't "turned up" at all! Instead, the new system brought boost on harder and faster than the electronic factory control.

So in this example you can see that full throttle acceleration increased in the mid-range but was unchanged elsewhere.

### Power

Let’s talk now about power. Since the measured on-road acceleration curve is exactly the same shape as the engine’s torque curve, and since power is measured by multiplying torque times speed, can we now calculate the shape of the engine’s power curve? The answer is yes.

Let’s take a look.

Here are the measured instantaneous acceleration figures for a small, fairly low-powered turbo car (taken of course in the one gear). The car was being tuned with programmable management – the table shows the instantaneous acceleration figures before and after fuel and timing changes aimed at improving high rpm power.

 RPM 2000 3000 4000 5000 6000 Before top end fuel and timing change (g’s x 100) 11 20 23 19 13 After top end fuel and timing change (g’s x 100) 11 20 23 22 17

(To make it easier to draw the final graph, I’ve multiplied the actual recorded g figures by 100. So a measurement of ‘11’ is actually 0.11g.)

A graph of this data makes the change in acceleration easier to see.

So the top-end acceleration is improved by the fuel and timing changes, but what does this look like as a power curve?

To find power, all we need to do is to multiple the acceleration by the rpm.

 RPM 2000 3000 4000 5000 6000 Before top end fuel and timing change 11 20 23 19 13 Calculated power before 22 60 92 95 78 After top end fuel and timing change 11 20 23 22 17 Calculated power after 22 60 92 110 102

(To keep the figures manageable on a graph, I’ve divided the final calculated power figure by 1000. That is, 11 x 2000 = 22,000, divided by 1000 = 22.)

Let’s look at the graph of this data.

Now we start to see how interesting the results are – and how small changes in torque at high revs really impacts power development.

So what can we see? Firstly, the figures on the vertical axis are arbitrary units – they don’t show either kilowatts or horsepower. However, even with these figures being arbitrary, we can still use them to make comparisons. It can therefore be seen that power went up at 5000 rpm from 95 to 110 units – that is, a 16 per cent gain. At 6000 rpm, it went up by no less than 24 per cent.

We can also see that power rapidly falls away after about 5000 rpm – so there’s not a lot of point in running a higher rev limiter.

Here’s another graph of measured acceleration and calculated power. This car runs a VTEC variable valve system that opens both intake valves when VTEC is activated (and runs only one intake valve when it is not). With the engine being run by programmable management, at what point should the VTEC be switched?

The measurements were made through the rev range with VTEC off and on, all at full throttle. The lines cross at about 2200 rpm – below this engine speed, VTEC should be off; above it, it should be on. Note also how VTEC operation nearly doubles power at 6000 rpm…. it sure needs that extra valve open!

(Incidentally, by using a throttle stop [eg a block of wood under the accelerator] these measurements could also have been made at say half throttle. Since VTEC is triggered by a 2D table using both rpm and throttle position inputs, this table could then be set up very accurately.)

### Conclusion

Especially if you like making your own modifications and doing your own tuning, this technique for measuring changes in power (and the shape of the engine’s power curve) is fascinating and useful. Free, too…