# Power measurement test bench in motorcycle tests

## Background to dynamometer measurement in motorcycle tests This is how power measurement works

Clamp the bike onto the test bench roller, turn the tap to the stop, and the power measurement is complete? Determining power and torque on motorcycles is not quite so simple after all.

Deafening noise penetrates the room. The engine roars its head off, and the two fresh air blowers whistle at the top of their voices. To do this, the exhaust gas extractor drones on. Nothing works here without hearing protection. We are on our test bench, where every test machine goes through the same procedure: Determine power and torque. These values appear regularly in the magazine as curves in a diagram. But how exactly does the power measurement work??

### power at the rear wheel

In simple terms, the system measures how fast a roller driven by the rear wheel accelerates. For this purpose, it records in which time the roll builds up which velocity. From the acceleration, the computer calculates the torque, taking into account the mass moment of inertia of the roller, and from that the rear wheel power. If you want to know exactly how this works, read the last section. In order for the computer to spit out how much power is available at which rpm, the tester taps into the ignition or rpm signal on the bike. When measuring, we always run the engines into the limiter in order to record the maximum speed.

### Power at the crankshaft

But how do you get from this to the power at the crankshaft?? This (higher) value is given by the manufacturers in their data, and we show it in the diagrams. Crankshaft power cannot be measured, only calculated. Two steps are necessary. First, the test bench determines the so-called power loss or friction power. It is generated in the drive train between the crankshaft and the rear wheel. It includes the secondary drive (pinion, chain, sprocket), the transmission and the clutch. Tires also cost power – very soft ones more, very hard ones less. The dyno calculates the power loss as soon as you let the motorcycle coast for a while with the clutch disengaged. This value is added to the rear wheel power, you already know the power at the clutch. Now just add two percent of this value, and the crankshaft power is ready. Example: A machine produces 200 hp at the clutch. At the crankshaft 204 hp are then available.

### Street tires instead of chunky ones

Why? In most engines, there is a gear ratio between the clutch and the crankshaft – another power guzzler. An EU directive puts this power loss at two percent.

To keep the power loss as low as possible, the testers always make sure that the chain is well lubricated, that the sag is correct and that the tire pressure is correct (about 2.5 bar). Coarse tires (Sportenduros, Crosser) are replaced by street tires.

### A desire for formulas and equations? Please!

If you’ve made it this far, you’ll be happy to know a few formulas and equations as well. Faithful readers may remember that we already discussed this topic a few years ago. Here again some technical knowledge to refresh.

As mentioned at the beginning, the test bench records the acceleration of the roller. For this, he needs two values: first, the speed difference of the individual measurements (∆v, pronounced: Delta-Vau) and second, their time difference (∆t, pronounced Delta-Te). The acceleration (formula symbol: a) is calculated like this: a = ∆v/∆t. Example: If the roller increases its rotation speed by four revolutions/second every second (in the first second it rotates four times, in the second eight times, in the third twelve times, etc.), the power is measured.), this results in an acceleration of 4/s². However, acceleration alone does not get us anywhere, we also need the mass moment of inertia (formula symbol: Q) of the test rig roller. Roughly formulated, this physical quantity expresses how much a rigid body resists being set into rotation or braked out of it. The mass moment of inertia is calculated from the mass (m) of the roller and its radius (r). The following formula applies: Q = m – r² – 0.5. Example: A roll weighing 1000 kilograms has a diameter of 46 centimeters (corresponds to a radius of 23 centimeters, = 0.23 meters). So the moment of inertia Q is 1000 kg – (0.23 m)² – 0.5 = 26.45 kg m².

The test bench computer uses this value to calculate the torque (formula symbol: M) with which the roller with the mass moment of inertia Q is accelerated by the dimension a. It is valid: M = Q – a. For our example this means

M = 26.45 kg m² – 4/s² = 105.8 kg m²/s². The unit for force (Newton, N) can also be written as kg m/s². Therefore: 105.8 kg m²/s² corresponds exactly to 105.8 Newton meters (Nm).

From this we can immediately calculate the kW output (formula sign: P) at a certain speed (formula sign: n). All we need is a constant that converts from revolutions per minute to meters per second. This constant is 60000/2π, so about 9549. π describes the ratio of the circumference of a circle to its diameter and is about 3.1415. It is valid: P = n – M /9549. If, for example, the 105.8 Nm are applied at 4450 rpm, the drive consequently produces 49.3 kW at this speed, which equals 67.1 hp. Because, as we know, one kW corresponds to 1.36 hp.

### Measured and calculated values

As standard diagrams we usually show the power at the crankshaft (diagram 01) and the torque (03). For this particular comparison, we superimposed the curves of the Kawasaki Versys 1000 (green) and the Yamaha MT-09 (red). Both machines have a similar peak power, but the displacement differs significantly.

They also play in a different weight league. In the diagrams 01 and 03 one sees the engine superiority of the Kawasaki up to the maximum output clearly. With a displacement surplus of over 23 percent (1043 to 847 cubic capacity), this is no great surprise.

Also with the tractive power in the third gear (04) the green one is still in front, but already more scarcely. The tractive force is that force which acts on the rear wheel. In contrast to the conventional diagrams, the total gear ratio (primary, secondary and gear ratio) is included in the tractive effort. So the Yamaha is a bit shorter geared than the Kawasaki.

Diagram 05 shows the acceleration. A purely mathematical value without driving resistance (rolling and air resistance). This value also takes into account the weight of the vehicle and represents the dynamics felt by the pilot. And look: Suddenly the MT-09 is ahead. At 192 kilos, the Yam is a whopping 63 kilos lighter than the Versys (255 kilos). The lower curve in diagram 02 shows the power loss. It is added to the upper curve (rear wheel power).

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