You can use 46 MJ/kg of fuel for the thermal energy content of petrol and 29% for break thermal efficiency of the engine. Weight difference due to KERS is at least 30 kg.
Here we go:
30 kg * 46 MJ/kg * 0.29 = 400 MJ per race equivalent mechanical energy from the engine
§ 5.2.3. regulates a maximum of 400 kJ/lap of energy output from KERS
400 kJ * 70 laps = 28 MJ
=> if the weight difference for KERS was carried in fuel there would be 14 times more mechanical energy available
=> KERS isn't efficient under pure racing considerations
That doesn't tell us whether KERS will save any fuel, but it is a very strong indication that it will not. You would have to go into a performance analysis to answer the question. It is generally believed that 10 kg will give you 0.5 s per lap. So a difference of 30 kg will mean you add 1.5 s to an average lap.
http://www.formula1.com/inside_f1/under ... /8763.html
F1 official web site wrote:KERS lap time benefits range from approximately 0.1 to 0.4s.
So even if we use the optimistic figure of 0.4 s we get almost four times the performance from not carrying the KERS weigt around.
=> from both comparisons that KERS is a political statement!
The purpose was simply to bridge a gap and show the commitment to energy recovery technologies until the new engine formula could kick in. The 2014 formula was much too difficult to implement quickly in 2008, so they went for KERS to bridge the gap.
The history of KERS and minimum weight:
- 2008, 605 kg, no KERS
- 2009, 605 kg, KERS possible but not feasible due to performance deficit
- 2010, 620 kg, KERS increasingly used
- 2011-2013, 640 kg, KERS is essential to all teams
- 2014, 690 kg, ERS is mandatory with kinetic and heat recovery
Having a look at 2014:
If we consider that the new power train weights in at 80 kg more than the 2008 V8 engines and saves carrying 40 kg of fuel we still have to make up 40 kg of extra weight by the ERS system. So lets have a look at those figures. The new system is supposed to keep the performance level or exceed it. So we can positively say that the system will save 35% of the race fuel.
The MGU-K can deliver 120 kW to the power train and theoretically itwould be legal to feed as much as that power from heat recovery and kinetic recovery. The figure is a bit unrealistic but we can use it for a back of an envelope style computation. We would assume that 120 kW would be delivered for 65% of the race duration of 90 minutes.
120 kW * 5400s = 648 MJ
40 kg * 46 MJ/kg * 0.29 (old engines without ERS) = 534 MJ
So our calculation shows that the new 2014 systems makes sense in every respect. It saves fuel and will earn the additional weight that it costs to implement in terms of energy recovery. Naturally such a system would also have been better in 2009 but at the time it was impossible to implement.