# KERS in F1, what does it offer?

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Will KERS make the car go faster in a straight line, the short answer was always going to be, No! With reference to article 5.1.3 of the 2009 regulations, the engine speed cannot exceed 18,000 RPM. Hence by knowing the different rotational speeds in the drive train, regardless of where KERS is, it cannot cause the engine to rev beyond this limit. As such top speed of the car will not be affected.

What we do see however is an increase in the torque that the car can in fact produce. For the purposes of this article, let’s assume that the torque curve for a formula 1 engine is constant (we know this not to be true) between about 9,000 and 18,000 RPM. For the purposes of this article we’ll assume for all rev’s to be within this range. So let’s compare the additional torque that KERS can provide to the car.

From the above power equation, and the regulations the Mechanical power of KERS is fixed at 60kW and hence torque is dependent on rotational speed. For the first case, let’s assume the cars are initially starting from the grid. Within moments the engines will reach and pass 9,000 rpm. In first gear at this time we can roughly assume that the cars will be travelling at approximately 75-80Km/h (~50Mp/h). At the same time, the engine will be making about 360HP (266kW) with a total torque at the rear wheels of nearly 4,150Nm (considering its multiplication through the drive train, by factor of 14.7-14.9) ultimately this results into a linear acceleration of 18.2m/s² (1.85 G). With all this acceleration 1.22 seconds later the car will then need to change gear into second at a speed of 150Km/h.

With KERS and its additional Torque and power at this speed (266 + 60 = 326kW) at this speed, we see the torque at the rear wheels increase from 4,150Nm to 5,095Nm, resulting in a straight line acceleration of now 22.4m/s² (2.28G) as a result of all this low down torque, the car will accelerate to gear change in a matter of only 1.05 seconds; assuming the rear wheels are able to maintain traction.

At a time of 1.22 seconds we can calculate that the KERS car will be only 2.2 meters ahead of the non KERS powered car. At these speeds the time difference is only .052 seconds; with nearly 20% of the total KERS energy used up for the lap as can be seen the difference is less than a car length. At a time of 2 seconds, the gap will open up to 4.53 meters, and a time differential of .087 seconds.

This almost seems barely worth the vast amounts of time and money that is invested into the technology. Considering that using KERS in one continuous 6.67 second period would only lead to a gap of only 21.85 meters, and a time differential of .28 seconds. It must be noted that in this analysis considering that KERS was deployed at 9,000 rpm, and at 75km/h in first gear, the cars have travelled an additional 392 meters (Non KERS) and 413.9 meters for the KERS car, with final speeds of 280 and 295Km/h respectively. One thing that we are not considering here is the ‘tow’ that the non KERS would be able to take advantage of by drafting the KERS powered car, so this .28 second gap, is a mathematical straight line maximum advantage, and explains why we have not seen these gaps in racing to date. We have also been assuming that the tyres are ideal and that they will hold under these immense torque values. We only need to look at the Circuit of the America’s in Texas where cars we’re still spinning the wheels in 3rd gear during practice sessions.

Irrespective of this we can see exactly where the teams got there figures from during winter testing when it came to evaluating the advantage of KERS, and the time advantage that this would offer on the track. We can see why it was claimed that not to have this technology would have been competitive suicide, however so far we are only seeing the power advantage of the technology. Below we can see the speed graphs and a rev graph of cars with and without KERS.

As we can see from the curves above, the advantage of KERS with respect to the ability to get the car into higher gears is obvious. Providing that KERS can be used indefinitely a car can reach can reach a top speed of 320Km/h at 18,000 in as little as 11 seconds after passing 9000 rpm, as opposed to 25.55 seconds in the non KERS powered car, and the additional torque provides more capability for acceleration however as discussed earlier the cars are limited to a maximum engine speed. As such any use once the car has redlined, will only allow the car to overcome additional drag and then engage the soft limiter.

Such use would in fact allow KERS cars, to run more aerodynamic grip through the corners, potentially leading to greater benefit, however by saving the KERS power for use at top speed, the cars will undoubtedly suffer under acceleration nullifying the use of the device out of slower corners, where its low end torque can be used most effectively. Evidence of this has been proven by the courtesy we all enjoy, being able to listen to Race Engineers telling their drivers to use KERS out of slow corners where the benefit is the largest. As such KERS will allow and does allow the cars to set lower lap times.

This article is the second in a series where we look at the KERS systems in use from 2009 to 2013. Read part 1 at http://www.f1technical.net/features/18603 . In part 3 Richard looks into the flywheel KERS option. Text by Richard Ronc, Ronc Industries