It is so, so important to me that people understand that Tim didn't figure out the bats because Dick was a "Show off". Like yes, Dick Grayson is the most flamboyant, dramatic ass man you will ever meet.
But the quadruple somersault? There's no way that was because dick was just showing off. Because you're telling me Bruce Wayne, who's so committed to hiding his identity that he literally acts like a completely different person out of the mask in public just to ward suspicion, would miss the fact that Robin regularly uses the flying Grayson's trademark move? There's literally no way.
In the comics we see Tim explain his deductive process to Dick and Alfred and they're both surprised impressed whatever. We don't see him explain it to Bruce. I think Bruce would be surprised and shocked that a 9 year old was able to put the pieces together but I don't think he'd be surprised that the quadruple somersault gave it away.
So if Bruce was possibly aware of such an obvious give away, why let it continue?
It really comes down to the physics
So Dick was 9 when he started out right? That means the most he'd have likely weighed was 43kgs or roughly 95lbs in freedom units.
But Dick and both of his parents are gymnasts who tend to be smaller. So he was likely less than that.
In physics, rotating objects build up angular momentum (this is how bikes stay up right for example). The more rotation, the more momentum. And objects with less mass build up that momentum much faster than those that are heavier.
Robin constantly has to fight people who are nearly 3 times his size. I teach 8 year olds, they're tiny. A quadruple somersault for a small boy that weighs less than a hundred pounds is a brutal weapon. Especially if you add in the acceleration from gravity as he drops in from above.
And I can guarantee you this logic tracks because Dick literally utilizes this idea, without the somersault, in the 2009 teen titans cartoon.
Yeah, that's right. We're talking about the infamous knee drop.
Like it is borderline savage. Add in a quadruple somersault and the resulting force is nearly fatal. It's likely the main reason Batman would ever allow him to do it with the cape on.
Also, Dick landing feet first on the penguin in the first image probably gave the guy severe back issues
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