Why does thicker metal take longer to cut?

You would never cut across the widest dimension--always the narrowest. You want to minimize the number of teeth contacting the material at the same time, maximizing the pressure on each tooth.
Actually, I usually cut the widest dimension because my cut will be truest. I sacrifice speed for accuracy. Sometimes, I will start a kerf along the wide side and flip it vertically to finish. The kerf helps to guide the finish cut. Another reason would be if the saw limits the cut. A 4 x 6 band saw won't cut a 5" wide piece if mounted vertically.
 
Actually, I usually cut the widest dimension because my cut will be truest. I sacrifice speed for accuracy. Sometimes, I will start a kerf along the wide side and flip it vertically to finish. The kerf helps to guide the finish cut. Another reason would be if the saw limits the cut. A 4 x 6 band saw won't cut a 5" wide piece if mounted vertically.

The kerf should be completely unnecessary if your saw is properly setup; this just prematurely wears out the blade. And, if the material won't quite fit in vertically, or is too thin for the tooth pitch, you would clamp it in the vise on an angle off horizontal.
 
The kerf should be completely unnecessary if your saw is properly setup; this just prematurely wears out the blade. And, if the material won't quite fit in vertically, or is too thin for the tooth pitch, you would clamp it in the vise on an angle off horizontal.
The saw is a Buffalo brand, Taiwan manufactured almost 40 years ago. The saw has always cut at a slight angle vertically and there is no means for adjustment. Believe me, I've tried.
I do clamp at an angle, usually when a piece is too large to fit (although the saw is nominally a 4 x 6, the largest horizontal cut that I can make is 5"). I prefer not to since it is not very stable and the work can pull out of the vise, potentially doing nasty things to the blade.
 
Say cut 1x5" metal. If cut 1", only the front few teeth cut it. So it takes less time for the teeth to go through the 1". Same for 5", it takes a lot of time to go through 5" at a same speed. The rest of the teeth just dangling there. In reality, maybe they all sink in a little, but the force is just not enough to push the whole row of 5". So maybe the front is pushed down a bit and the back. Saw cutting is somewhat similar to lathe cutting, a few thous here and there make a big difference. So if the saw blade don't bite down, it wouldn't cut much. For a wide piece, it's hard to force too much, and the teeth wouldn't bite down either. Like lathe, it starts out below the surface to cut. If we do a plunge cut, it works, just not so good, and that's an equivalent of 1 tooth. Plunge cut of 20 or 50 teeth must be very hard, and that's why it's much slower. It just doesn't cut deep enough. I think if people want to experiment, they can try both and compare the shavings. I don't think they're the same.
 
A single tooth at a constant speed and constant down force into material will cut at a constant rate. Double the amount of teeth in contact with the work and you need twice the down force at the same speed to keep each tooth cutting the same amount. Ten teeth will cut twice as fast as 5 teeth if down force (per tooth) and speed is held constant even though EACH TOOTH is cutting the same amount as before. Being as nothing is free in this world, more teeth cutting and more down force will require more power or the speed will drop and all then bets are off. I hope this helps you because I didn't actually understand your question.
 
A couple of guys have hit the nail on the head, to answer this question is is useful to imagine theoretical extremes.
If a saw blade of infinite strength, length and rigidity and with a set 40lb cutting pressure is set to cut a 1/8" metal work piece cutting will be very rapid, make the work piece close to the length of the blade and the pressure per tooth will barely mark the metal.
 
The tooth design (and edge character) on the blade will determine the results. A twist drill sharpened for steel neither pulls into nor pushes
out of the cut, but self-feeds with relatively low applied force, in steel. It dives into copper, however, or brass or lead.
Similarly, a slightly dull blade requires pressure (and lacking pressure to take at least a few mils per tooth, it will just heat
the cut and not penetrate at all). So a dull blade won't bite along a long kerf (as in the five-inch dimension)
though at similar feed pressure it might cut the 1/4" dimension adequately.

A blade on a bandsaw won't apply uniform pressure on all its teeth for the whole length of a five inch cut, unless
the blade is stiff (like a 3/4" blade depth, rather than a 1/2" blade depth) . That's what blade flexure does to you.
 
I had to do a bit of shopping today and this article was on the start page of one of the local suppliers. It has a formulae so you can work out how long a cut will take.
 

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Rocking(changing the angle) the hack saw every few strokes allows one to cut thick material easier. This is because the angle
change reduces the number of teeth cutting at any one time. Less teeth cutting increases the pressure on each cutting tooth
resulting in more material removed with each stroke.
 
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