I was speaking with a mechanical engineer (i'm a student in the same major) about handlebars. We kind of agreed that unless you bend your bars past the elastic limit, they'll remain the same shape when you are sprinting, even if they "flex". Therefore I said that people using steel bars is just for "feel" preference, but i want to hear some arguments that say that they truly are faster because of better power transfer.
I failed out of mechanical engineering so I have no street cred in saying this, but if the racer flexes an object, and that object is not part of the power transmission between pedals and rear wheel, wouldn't that force be spent doing something other than propelling (or accelerating) the bike?
In other words, if I pull up really hard on the bars and I flex them a good, say, 2 cm, and that takes 100 pounds of force, wouldn't that be a lot of wasted energy on my part? If the bars didn't flex, I'd be counteracting my leg's attempt to lift me up, and therefore I'd be pushing down harder on the pedals.
Granted, once the bar flexes until I can't flex it anymore, the force will be used to counter my foot and therefore force the pedal down harder. But during that instant of bar flexing, the bike won't accelerate as hard.
Unlike arguments for flexing frames, wheels, and such, the handlebar springing back (i.e. releasing the force input by the racer) will not help the bike accelerate because most racers don't push down as hard as they pull up. I know I don't.
Is that worth a C- in engineering? Okay, D- because I have no supporting equations to prove my ramblings.
Note: I use relatively flimsy aluminum bars on my track bike (heat treated 3ttt AL, very lightweight) simply because that's what I had that would fit the stem I wanted to use. I do use a steel stem (tubular welded) because it's stiff, but primarily because it's the right size and I had it laying around. However, the "good" riders put out crazy wattage (1800 - 2000 watts, apparently), and when you're dealing with those numbers, I think rigidity counts.
Also, I couldn't find it quickly, but there is at least one picture of a guy breaking his bars as he accelerates from the line. It's an older picture, I first saw it in the late 80s, but someone showed me that when I questioned the wisdom of heavy, uncomfortable steel track bars.
Not sure if stiffer bar/stem combo is objectively faster, but it's definitely a lot nicer not having flex on the front end when you go to torque the bars in a sprint because you can hold a more confident line. Going balls to the wall and feeling your front end flex is lame... the mind should be completely focused on putting power into the pedals at the crucial moment, and anything drawing it away from that is a disadvantage ATMO. I do a lot of seated rows in the gym in the off-season too to aid in torque. Anyways, haven't had a problem with Thomson to Deda Pista.
Just because they stay the same shape doesn't mean they are transferring power the same. Try riding with your bars loose at the bar to stem interface. Just loose enough that they will move easily, but tight enough to not slide side to side, you can keep control. You will be able to ride and you could even get used to it. You wont be able to ride the same, even though the bars are staying the same shape.