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So, I have not seen any talk of shooting with elevation and a hopup. I suspect we can expect the round to behave a bit differently when shooting up or down from level. Especially for those silly, inefficient BAR shooters with their tiny refire, it might be something really good to know about before the first shot is made.

Is there a significant effect?
 

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Okay, so I re-did all of the calculations, and this is what I came up with.

You should familiarize yourself with the Magnus Effect, which is basically the reason hop-up allows the bb to hop. Magnus Force, the result of hop up spin, is always perpendicular to the velocity of the bb in airsoft, meaning on a bb flying parallel to the ground, the magnus force is vertically upwards, 90 degrees with the ground.

Since magnus force is an upward force, and gravity is a downward force, on a bb that is travelling parallel to the ground, the two forces cancel out. The result is a flat trajectory.

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Here's basically a guideline to the variables and conventions:

g = force of gravity. It always points down (duh).
Fm = magnus force. It's always perpendicular upwards with the velocity of the bb.
θ = angle between the ground and the direction the bb is shot. If the bb is shot parallel to the ground, θ is zero. If the bb is shot upward, θ is positive. If the bb is shot downward, θ is negative.

Also, you probably know what absolute value is. Basically, it takes the value of a number and makes it positive. You represent the absolute value of value with a line on each side like this: |value|. So, absolute value of -95 is |-95| = 95, and absolute value of 95 is |95| = 95.

Hopefully you also understand what the magnitude of a force is, which is basically the strength. You represent the magnitude of a force with two lines on each side like this: ||force||. So, magnitude of Fm (magnus force) is ||Fm||. Don't confuse it with Absolute Value, which is only one line on each side.

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So, now that we have established all of that, here's how it works. I'm going to skip all the calculations and go straight to the point:
*(by the way, I'm completely ignoring wind and air resistance right now, which is weird because magnus effect depends on both, but I'm simply stating the principle)

We can say that the domain of θ is in between -90 degrees and 90 degrees for simplicity's sake. I'll repeat again, at θ = 0 degrees, the bb is fired parallel to the ground. At θ > 0, the bb is fired upward. At θ < 0, the bb is fired downward, .

I'm going to use the quote boxes to make it easier on the eyes.
If the hop up on the bb gives it a flat trajectory when fired parallel to the ground, then that means:
||g|| = ||Fm||
magnitude of gravity equals magnitude of magnus force. The two cancel out.
That means:
-when |θ| = 0, the bb will remain flat.
-when |θ| > 0, the bb will curve up, curving more as |θ| increases.
If you have overhop, aka when the bb is fired parallel to the ground, the hop up on the bb makes the trajectory curve upward, then that means:
||g|| < ||Fm||
magnitude of gravity is less than magnitude of magnus force, so the bb curves up.
That means:
-when |θ| = any number within the domain, the bb will curve upwards, curving more as |θ| increases.
If you have underhop, aka when the bb is fired parallel to the ground, the hop up on the bb makes the trajectory curve downward, then that means:
||g|| < ||Fm||
magnitude of gravity is more than magnitude of magnus force, so the bb curves down.
That means:
-when |θ| = arccos( ||Fm|| / ||g|| ), the bb will fly flat.
-when |θ| > arccos( ||Fm|| / ||g|| ), the bb will curve upwards, curving more as |θ| increases.
-when |θ| < arccos( ||Fm|| / ||g|| ), the bb will curve downwards, curving more as |θ| decreases.
Lastly:
-when θ = 0, the bb slows down solely due to air resistance (yes, NOW I mention air resistance...).
-when θ > 0, the bb slows down at a faster rate than it would if it were solely air resistance.
-when θ < 0, the bb slows down at a slower rate than it would if it were solely air resistance.
Air resistance and wind may possibly change the results though. Yes I understand that was long. If you need proof, learn about the magnus effect, and try it out yourself.
 

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Very nice description of how the magnus effect, gravity, and shooting angle affect how much the bb curves, lulukchoo23. I learned a lot from that. I knew the bb would curve up more at a higher angle, but I didn't know the how. Thanks for taking the time to write that.

@ Libelle- What exactly is a refire? I've never heard the term before. And why are you calling my rifle silly and inefficient?
 

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Masterjuggler - By re-fire i believe he is talking about the time to get your follow up shot in
the air.

Lulukchoo - Amazing write up, thank you. Also, do you mind if I cross post this over to my teams forum to better educate fellow players? all credit will be given.
 

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Yeah, as long as I get my credz, you're more than welcome to. Just keep in mind that the difference between hop isn't like, extremely drastic. At least, not unless you're seriously over or underhopping lol.
 

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Masterjuggler - By re-fire i believe he is talking about the time to get your follow up shot in
the air.
That makes sense, thanks.

You know Libelle is a woman, right? Or at least if I'm remembering correctly.
 

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I think Lulukchoo's post should be put in to a seperate thread and stickied, or perhaps we should make a thread that explains many of the concepts of the science behind airsoft. I think there is a thread somewhere here that was a copy of The Airsoft Trajectory Project (property of cybersloth.org http://mackila.com/airsoft/atp/), it could be added to that along with the science behind R-hop and stuff. (Sorry to go off-topic.)
 
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