# What does data about kWh in the French Open "shots of the day" videos mean?

The French Open publishes on its YouTube videos with "shots of the day" - the most impressive plays from a particular day at the tournament.

At the end of the point, an information about kWh is shown. For instance after this lob of Ramos in the match against Sock, the following data are shown:

41 forehand winners, 184,5 kWh.

What is this information supposed to represent? It would be especially nice if some official source about this can be found. (By "official", I mean from Roland Garros' website, the video sponsor, or the stats provider.)

• These kWh messages are obviously a message from the sponsor, ENGIE. As far as I can tell, they seem to honestly believe the kWh values show some kind of “value” of the sport performance, cf. their page promising “Once the game is over, [the visitor’s] movement speed will be converted into kWh.” May 30 '16 at 14:12

To extend Fillet's information... to hit a winner, ΔKE would be Δ1/2mv^2, or a total of mv^2 (if players hit at similar speeds). I see suggestions [1] that typical shots are in the 60-80 mph range in men's tennis, and some winners get near 100 mph.
So .057*30^2 (for 70ish mph) is 50ish Joules per winner. 41 winners would only be 2 kJ or 0.0006 kWh. Even 100 mph for every winner, that's only 5 kJ = 0.001 kWh. So that doesn't work as anything significant.

I'm not sure what Fillet was taking from cyclingweekly (seems to be basically W/kg and to get to kWh, so you'd need to multiply out by mass and then hours expended to be useful)... but alternatively [2] shows 300-600 Calories per hour is a reasonable amount exerted playing tennis. That'd be 1/3 to 2/3 of a kWh each hour per player. So a three hour match easily could burn 3-4 kWh combined between the two players. Can probably get to around 10 kWh in a long pro match, but still an order of magnitude off.

One thing Fillet didn't consider is the total shots in the match. I found http://www.tennisabstract.com/charting/ and looked through quite a few... most I got was the Djokovic-Murray 2012 US Open, with just under 2000 shots (add the listed total of shot types for the two each players). At the 70 mph earlier estimate, we're still only talking about 0.02 kWh. Still no useful contribution (makes sense, considering how light a ball is). Seems we're usually tired at the end from running, not from swinging our arm.

So, I too can find no way to get near the values they show.

The only guess I can think of is that they actually mean kW (power) rather than kWh (energy). I saw rough estimates that the impact of a shot lasts a few milliseconds [3]. That seems reasonable. A 70 mph winner could thus be about 13 J/0.004 seconds, ~ 3 kW. 133 kW total for 41 winners. Finally a number\unit that sounds similar to their answer... though that would vary hugely by speed and contact time, and be tough to reasonably calculate?

Long story short, I'm as confused by it as Fillet.

• I was using mainly the sentences from the article such as "460W upper limit suggested above [for Lance Armstrong] for an hour-long effort", to justify that 1KW is beyond what a tennis player could ever output. Jul 11 '16 at 9:33
• Certainly is a confounding set of info... The more I've searched, the more I've seen sites interested in comparing running and bicycling (even bicycles.stackexchange.com/questions/9764/…)... but most seem more interested in emphasizing the skill of one or the other. But appears the focus on your site and most of the other is on the OUTPUT. Running, cycling, whatever, have inefficiencies... and I think think they're focusing on result rather than effort. Jul 12 '16 at 15:39
• 1 kWhr = 860 Calories. A lot, but doesn't seem crazy for an hour? bicycling.com/training/weight-loss/… shows a 200 pound man cycling 14-16 mph burns that in an hour. And quite a few forums suggest 15 mph is a reasonable rate for a starting cyclist. mensjournal.com/health-fitness/nutrition/… seems to match the running and cycling possibilities of burning a fair part of a kWhr each hour. So only guess I've got is your article focuses on the cycle's Watts rather the person's? Jul 12 '16 at 15:51
• Yes, I think (in)efficiency is the difference. According to wikipedia "The efficiency of human muscle has been measured (in the context of rowing and cycling) at 18% to 26%", en.wikipedia.org/wiki/Muscle . 460W is the power transmitted to the bicycle, but the athlete will need to burn 4-5 times more energy to achieve this. Jul 13 '16 at 6:34

I'm not sure if this should really be an answer, but it was too long for a comment.

Given a tennis ball mass of 57g, it is not the kinetic energy of 41 forehand winners.

Given 184.5kWh you have enough energy to accelerate 41 tennis balls to a velocity of 53000 mph.

It is also not the energy expended by the players in the match, as 1 kW is more than an athlete can output over an extended time, and the match can't have been going for hundreds of hours.