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Contributors to this article include:
Jeff 'Dr Strangelove' Ridgway,
What
is hop up?
'Hop-up', short for 'higher operating power', is a method of allowing a bb to travel further without imparting any extra energy into the bb. This is done by imparting a spin on the bb.

Without Hop-Up

With Hop-Up
Hop up works by the means of a rubber seal in the barrel of an Airsoft gun, that creates grip on the top of a bb as it passes through the seal. The friction on the top of the bb is greater as it has to overcome the rubber seal. As there isn't a seal on the bottom of the barrel, the bb is made to "roll" under the seal, causing it to spin.

The backspin allow the bb to counteract the pull of gravity for a short while, thus allowing the bb to travel further than a bb without any spin.
The basic mechanism that allows a bb with backspin to travel further is the same as that that makes aircraft fly - air pressure.
When a ball passes through the air with out spin, the force from air pressure on the top and bottom are equal and so cancel each other out, therefore causing gravity to take over and pull the bb to earth.
With spin however, there is some difference.

When any type of ball is given spin, there will be a small force on the side of the ball which is rotating towards the shooter/thrower.
For example. A boy throws a ball with left spin, i.e. the ball is rotating anti/counterclockwise. The left side of the ball is 'coming towards' him. There will be a force pushing the ball to the left. The same with hop. The ball rotates up, therefore creating a force upwards.
Now, this is all to do with air pressure. Applying spin on a ball in a vacuum is useless, as there is no air.
The force is due to decreased air pressure on of the ball rotating towards the shooter. This is because the air is being accelerated on that side of the ball. The acceleration of the air causes a drop in pressure, and as the air is not being accelerated on the other side of the ball (it's being deflected), the pressure doesn't drop on that side, so the increased pressure pushes the ball in the direction of lower air pressure. This mechanism is known as the Magnus effect, and is the same effect that makes golf balls go father, and what tennis players use to get the ball arc towards the ground faster.
A secondary effect to this a force due to turbulence from the spinning ball.
If a non spinning ball is thrown through the air, it will create turbulence behind it. But, as the ball is not spinning, the turbulence will be symmetrical behind it, and there is no net effect on the ball.
However, when the ball is spinning, the air coming off the ball is pushed to one side behind the ball, and the 'untouched' air will try to counteract this asymmetrical turbulence, creating a force on the ball, also in the direction of the force due to air pressure.
This secondary effect is known as the "Wake Deflection Effect"
So, in hop up, the bb is given backspin. This causes the air pressure above the bb to drop, hence allowing the greater air pressure below the bb to cause an upward thrust to the bb. This can be seen if you turn the hop on your weapon too high, and the bb will fly upwards.
The bb's spin will eventually drop away, as will the force holding it aloft. Then gravity takes over, and pulls the bb towards the ground.
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