I've designed industrial mechanisms, but not bikes. Sometimes, over-spec'ing the motor makes sense. You don't have to feed it all 2400 W. But the bigger motor might be easier to cool, have other advantages such as more convenient mounting and the right size spindle, and so forth. Counterintuitively, below a certain size, motors start to get more expensive. And using a catalog motor avoids having to spec a custom motor in order to get everything you actually want.

The decision to select this motor was mainly driven by what is available, price, dimensions and the size of the output shaft. The gearbox would not fit anything that has an output shaft smaller than 6mm. I knew that I'm not going to need all the power and also top speed.

The motor is only 2400W with sufficient cooling, which this design does not appear to have.

Yeah that was my first thought too. That motor isn't going to be happy running flat out for very long.

Does the movement not generate enough cooling from wind? Do you need heat sinks or active cooling?

They're designed for planes and the prop drives significant air for cooling. You could replicate this if you wanted, but it would be really hard to draw enough power to overheat this. You'd have to be going up a long steep mountain or be going ludicrous speeds.

One word: Hills.

Not sure why you're being downvoted. Though it's not JUST about hills.

I have a 2500W Luna Cycles fat bike (52V BBSHD mid drive motor and 12 speed drivetrain). It climbs hills effortlessly. It powers through sand and snow. It's been a lifesaver on uphill technical singletrack when I've had to stop and a blip of the throttle gets me going when I wouldn't have been able to just with pedal power.

I have no idea what the top speed of the bike is and don't care. 90% of the time I'm doing under 20 mph and almost all of the remaining time I'm doing 20-30 mph. I've ridden 750W hub drive bikes and they're not even remotely comparable. This is what people who cling to the antiquated eBike class ratings and watt limits don't understand. It isn't about top speed (I think doing >35 mph on a bicycle is crazy) it's about torque application in circumstances that demand it. I'm considering upgrading it to a 72V battery and 4000W controller.

I should have added heat as well. Having a motor rated for twice what you actually use helps keep things cool and running longer. Luna Cycle is a great company BTW.

I've got a 750w and it handles hills pretty well. To the point where you don't need to actually pedal unless it's a long steep one but even then it's like pedalling on a straightaway (using pedal assist is of course is always optional).

Before I got the bike I wanted the most powerful one available but I realized after getting one you don't really need that. And it's actually kinda dangerous, even for a experienced cyclist who's used to speed.

Even the standard tier batteries are more than enough for any urban biking in terms of distance. I rarely use even 20% at 48V, 10.5A.

An average "likes to do a couple 40 mile sporty bike rides a week" cyclist probably can do around ~150-200W continuous and maybe peak for 10-15 seconds at around 750-1000w. A hill that takes 20-30 seconds to climb, less than 500W most likely. Depends on their weight and training.

Cargo e-bikes tend to be at or less than around 1kW. 750W is still considered fairly powerful, and 500W is much more typical and still plenty enough for even a cargo bike to get up a hill, with appropriate gearing. 250W is about the standard for low-end e-bikes.

2.4KW is gross overkill, especially if you're not doing direct drive. More watts just means you can go up the hill faster. This assist motor is driving the wheel through the rear derailleur so it potentially has a pretty wide range of gearing.

250W pedal-assist only is all you can (legally) get as a bicycle in Europe. I have only one friend that can sustain 250W for hours (on a road bike), and he's a serious everyday "bicycle is the default vehicle" type. 250W is plenty for casual rides. Not judging the choice here, though, must be quite a beast ;)

To note is that these 250W are a relatively weird "continuous/average power" rating. There is lots of leeway in calculating this and peak power can be a lot higher, so a legal pedelec might easily deliver 750W while you accelerate or go uphill.

That is true, 250W-rated electric engine can supposedly make 1kW for some time without damage. But if I understand correctly, EU law prohibits the "power driver" to deliver more than 250W.

2,400W is around (and possibly more than) what the strongest track cyclists can sustain for about five seconds.

Tour de France cyclists racing up mountains generally sustain around 400W, which is enough to go 25+km/h for hills that aren't too steep.

A small correction here, generally the power output of climbers is measured in W/kg, not pure Watts, because their weight heavily influences their ability to climb. I think top climbers have around 7-7.5W/Kg. Even in these conditions, the power output of that motor is orders of magnitude higher than what a human can do.

You're right about the numbers often being expressed in W/kg, because power to weight is more important than power when going uphill. For big climbs (more than half an hour or so), that number is closer to 6W/kg for the best, or maybe a little more (especially if you go back in time a bit for some reason…).