The popularity of Octane and the theory that some cars "just hit harder" explained (car on ball physics facts and myths)

Quick tip: There's a summary at the bottom if you don't want to read through my rambling.

Yesterday I had made a post questioning if rotational velocity affects the power of a shot--in other words, do you hit the ball harder if you're spinning round and round with a long-nosed car--and while there certainly was a fair bit of interest and discussion, there wasn't really any conclusive evidence. Being the overly curious bastard that I am, I wasn't really satisfied with the unsure answers, so I set forth search through posts, watching youtube videos, bugging users on the Rocket League Mods discord, digging through code, setting up in-game tests, and staring at replays until I finally felt I had what I was looking for.

This is what I found:

Most of you are probably already aware that a car's hit box is just that: nothing more than a box. The way this box and the ball interact is weird from a "real life physics" perspective, but actually fairly simple when broken down. Some of you might already be aware of this, but stick with me in case you've unknowingly picked up any misconceptions about it:

1. The engine first determines the difference in speed between you and the ball. It saves that speed as the amount of force that will be applied to the ball. (Mathematically, it subtracts your vector from the ball's vector and saves the magnitude of the resulting vector.)

2. To determine the direction that force will be applied in, the game draws a line from your car's center of mass--which I will explain in a moment--to the center of the ball. The resulting direction is which way that force will be applied. (So it gets the vector between you and the ball, normalizes it, then multiplies its magnitude by the number from step 1.)

It's important to realize that because of this behavior, you can get results that simply make no sense from a real world perspective. For example, consider trying to pop the ball into the air by jumping under it, like so:

https://gfycat.com/WindyHappyAzurevasesponge

Makes sense so far; you hit the ball from below, and all of your momentum was traveling upward, so it goes straight up. You didn't hit it hard, so it didn't go very far either.

But what if we hit the ball from beneath going supersonic? Specifically, what if we time our jump so that our center of mass is still directly beneath the ball as we hit it?

https://gfycat.com/IllfatedPreciousGalapagoshawk

Real world physics says that the ball should gain the same height as the first gif, as we are only applying the same amount of upward momentum, yet that is clearly not the case here! However, if we break things down based on the two steps above, it makes sense: our speed is ludicrously faster than the ball, so the force we apply is huge, and our center of mass is directly below the ball's center when we hit it, so all of that force is applied straight up.

In fact, if we hop so that our center of mass is a bit further forward when we connect with the ball, we can even hit the ball high in the air backwards because of our forward momentum:

https://gfycat.com/HappyUnripeHind

So that's all well and good, but how does this tie into hitting the ball harder?

Well, let's get back to that center of mass. Each car has an arbitrary point that it rotates around while in the air; this is considered its center of mass. Each vehicle's center is a bit different; some are farther forward, backwards, up, or down than you might expect.

In theory, you want a center of mass that's as far away from the ball as possible; the more distance between that center of mass and the ball, the easier it is to adjust the angle of your hit. Simply put, if the center of mass is right up on the ball, even smaller positional adjustments result in a much different hit angle. (See: [This horrible I-never-claimed-to-be-an-artist example.] (http://i.imgur.com/r8r9iUQ.png))

Most of the time you're going to be hitting the ball forward rather than backwards. As such, you generally either want a center of mass that's further back, as that keeps it further from the ball, and makes aiming more forgiving. Unsurprisingly, most of the popular cars--Octane, Dominus, Breakout--have a center of mass that's noticeably further back than most other cars. This brings us to the first reason that popular cars seem to hit harder: it's not that they hit harder, but rather that they are much easier to consistently hit hard with.

Think about it: with a center of mass that far back, you don't have to worry so much about lining your car up with absolute precision; you can stand to be a tiny bit off with your shots. Cars with a center of mass much closer to the front of the vehicle (e.g. Scarab, Grog, Backfire) demand much more precision; otherwise the ball is going to glance off in a direction you never intended. There's nothing stopping them from hitting just as hard, but they're far more fickle.

Right, so that's all well and good, but what about that rotational velocity stuff that got me into this mess in the first place?

Well, it turns out from a pure code standpoint, there's nothing that says a longer-nosed vehicle should hit harder. There just isn't! However, that's not the end of the story.

The truth of the matter is that while a longer-nosed vehicle will hit with the same exact force as any other, it's possible to get more hits before the ball makes it out of your range.

Think of it this way: As a car is rotating through the air and comes in contact with the ball, it's going to impart a good portion of its speed right then and there. However, if the car keeps rotating--and is rotating fast enough--it's possible that the nose (or some other edge) could catch up to the ball before it's traveled out its range. This gives you a 2nd (or more!) opportunity to impart more of your speed to the ball, resulting in a stronger hit. Just how much stronger though?

Realistically, probably not too much. Consider that the two-step hit formula above calculates the force as the difference between your speed and the ball's speed; right after that initial hit, the ball is already going to be pretty close to moving the same speed as you. Likewise, the more speed you put on the ball initially, the less likely it is that your car will be rotating fast enough to catch up for that 2nd hit. Most of the time these 2nd/3rd/etc hits will occur when the initial hit is pretty weak--and you can't really expect a weak first hit to be followed by anything stronger.

That said though, while it's a small advantage, it is an advantage. Cars that will excel at this are generally wide (hello Octane, Batmobile), flat (hello Batmobile, Dominus, Breakout), and have a relatively long nose (hello Dominus, Breakout, and even to a lesser extent Octane when you consider how far back its center of mass is). Basically think anything that has an easy time flicking; it will probably also have a better chance at getting those extra touches. It's not a huge advantage, but every little bit helps; as little as it is, it could mean the difference between scooping the ball away from an opponent's clear, after all.

Finally, a fun fact and potential useful tip: Nothing I found implied that any part of the car (other than the wheels) is more/less powerful than the other. The front, back, sides, and top of the vehicle all hit with equal force; the catch is that not only are you significantly more likely to line up with your center of mass properly when hitting with the front of your vehicle (given that your nose has a much smaller surface area than your hood), but it's pretty unusual to be traveling at top speed in any direction other than forward. You can take a power shot with the hood of your car... but good luck lining up that sweet spot while traveling supersonic hood first.

And that... well, that was far larger of a post than I expected it to be. But hey, knowledge is power. Let's summarize, as well as throw in a few extra bits and pieces I couldn't find a place for in that wall of text:

SUMMARY:

1. Having a car with a center of mass further back makes it easier to consistently hit strong well-aimed shots. (Though every car can hit just as hard if your aim is good!)
2. Having a flat, wide, long-nosed car can make it easier to get extra touches while rotating, effectively transferring more power to the ball. (Though these extra touches will generally only have a noticeable impact on weak shots.)
3. Pro favorites such as the Octane, Dominus, and Breakout tend to follow one or both of the above two points, quite possibly explaining at least part of why they're considered such good vehicles.
4. All sides of the vehicle except for the wheels can hit with maximum power provided you line up your center of mass with the ball. (The front is just generally far easier to do this with, especially at high speeds.)

Feel free to hit me with any questions. I hope this helps!

EDIT: Good lord, I did not expect this post to blow up like this! I'll be doing my best to respond to the majority of the posts and questions that I've not yet gotten to over the next few hours. Thank you all very much; I'm glad I could help. :)

It's a bit late, but I also want to give a shoutout in particular to Rocket League Science over on YouTube. They aren't the only source I used when research this, but they're one that has a surprisingly low amount of views for the level of quality and research that they put into their videos. Go check them out!