Can someone tell me why a reduction in back pressure (i.e. from removing resonators or permanently opening the butterfly valve on the muffler) results in reduced low end torque?

 

Just imagine that when you seal the exhaust pipe, the exhaust cycle will have to over some the air pressure from seal exhaust pipe.
Remember Newtons' third law? Ideally, when one object applies some X amount of force on a stationary object, the object applied the force will receive the same X amount of force that it applied to the stationary object. However, in case of back pressure, it's the X - (some force absorbed by compressing air) apply back to pistons' force.
Ideally, if there is no back pressure meaning that you take the exhaust system out, Torque = Fxd
However, because of back pressure, let's say it's F'
=> Torque = (F - F') x d
So you see that Torque is reduced.

Disclaimer, I got a B- in physics, so chances that I got wrong very high. Please correct me if I'm wrong

 

However, it results in increased horse power.

 

It's not a simple explanation, but I'll try.

First of all, increased back pressure is not good. Ever. At any rpm. As my530i has posted, all it will do is reduce your torque and therefore power.

Secondly, as far as I can understand it, exhaust resonators largely exist to decrease noise. They may also work at very specific rpm to increase (or reduce!) torque, but they only work for that within a very narrow rpm band. The principle for both a resonator and the butterfly valve is the same, and it is based on the following:

What you want from an exhaust system is two things:

1. Quick evacuation of the exhaust gases from the cylinder
2. The highest possible speed from the exhaust gases to be maintained for as long as possible.

Point 1 is pretty obvious. Mixing exhaust gases with fresh ones will decrease power as exhaust gases do not release any power when they burn again.

To understand point 2, you need to consider that gas pressure at the exhaust valve is not constant, but travels in waves of high pressure at the front followed by low pressure (in fact negative pressure). These waves of negative pressure are useful in as much as they will suck in fresh intake gases when both exhaust and intake valves are open, and they will keep exhaust gases flowing out even when cylinder pressure has started to decrease owing to the piston moving downwards during the intake stroke. The negative pressure is greater the higher the speed of the gas down the exhaust pipe.

The speed at which these pulses move down the exhaust pipe is dependent on the amount of resistance (back pressure) that the exhaust system exerts. For an individual pulse, this is roughly inversely proportional to the pipe's diameter (larger pipe = lower resistance). But when you have multiple waves, the speed is also dependent on how well "coordinated" these pulses are. If you can get a high pressure wave front right after a low pressure wave tail, they will travel faster than if you get the waves bunched together or far apart from each other. Maximum speed is achieved when the front of a wave is exactly after the tail of the preceding one and you get a train of waves travelling down the exhaust pipe.

At low rpm the waves are further apart from each other, so you want an exhaust system with a smaller diameter to "slow down" each wave so that the "train" speed is maximised. At high rpm, with more frequent pulses, you want a larger diameter. In theory, you would need a diameter that is infinitely adjustable with engine speed to always maintain optimal gas speed and thus maximise the evacuation and scavenging effects of these pressure pulses. In practice, you will always reach a compromise depending on whether you want to enhance driveability at low rpm ("narrow" exhaust) or performance at high rpm ("broad" exhaust).

The butterfly valve allows the engine to have - within some limits - the best of both worlds by providing a smaller exhaust volume at low rpm and letting the engine breathe at higher rpm.

Hope this is clear...