Percentages are of the belt, not of the conveyor
A conveyor with 300 ft centres has roughly 608 ft of belt in it once the wrap round the pulleys and the take-up is counted. Elongation figures on a belt datasheet are percentages of belt length, so a 1 percent elastic figure is 6.08 ft, not 3 ft. Applying the percentage to the centre distance halves the answer, and it is an easy mistake because the centre distance is the number written on every other drawing.
The four things that add up
At the defaults: 1 percent elastic gives 6.08 ft, 0.4 percent permanent gives 2.43 ft, one re-splice at 30 in gives 2.5 ft, and 0.2 percent of cut tolerance and installation slack gives 1.22 ft. That is 12.23 ft of belt to be accounted for. The carriage moves half of it, 6.11 ft.
The elastic term comes and goes with tension and the permanent term arrives once and stays, but a take-up has to hold both at the same time unless the belt is going to be re-spliced, which is why they are added rather than compared.
The factor of two
Two strands of belt run to a take-up pulley. Move the pulley a foot and the belt path changes by two feet. A screw take-up at the tail behaves identically, because pushing the tail pulley back adds length to the carry run and the return run at once. So carriage travel is always half the belt length being taken up, and the same factor of two runs the other way on a gravity counterweight: the weight is twice the slack side tension, because each of the two strands carries half of it.
Splices matter more on short conveyors
A splice consumes the same 30 inches whether the belt is 80 ft long or 800. At 300 ft centres it is 20 percent of the travel; at 75 ft centres it is right about half. That is why short conveyors are so often re-spliced rather than given long take-ups, and why the same take-up design scaled down stops making sense.
What is not here
Temperature, which moves a belt in both directions and is not small on an outdoor conveyor between summer and winter. Whether the stroke you have is enough, which depends on things the page does not know. And what the slack side tension ought to be, which is a drive and sag question rather than a length question — the counterweight line here doubles whatever number you give it and has no opinion about where the number came from.
Questions people ask
How much take-up travel does a conveyor belt need?
Add the elastic elongation at working tension, the permanent stretch over the belt life, whatever a re-splice consumes and whatever cut tolerance you want to absorb, all as lengths of belt, then halve the result to get carriage travel. At 300 ft centres with a 1 percent elastic and 0.4 percent permanent belt that comes to 12.23 ft of belt and 6.11 ft of carriage movement. Whether that is the right stroke for your machine is a question for the conveyor maker.
Why is take-up travel half the belt stretch?
Because the belt wraps round the take-up pulley and comes back, so two strands run to it. Moving the pulley one foot changes the length of both strands, which is two feet of belt. A screw take-up at the tail pulley does the same thing for the same reason, since moving the tail lengthens the carry run and the return run together.
What is the difference between elastic and permanent belt stretch?
Elastic stretch appears as soon as tension comes on and disappears when it comes off, so it is a working range the take-up has to move through every time the belt starts and stops. Permanent stretch is the break-in elongation that never recovers, and it consumes travel once and keeps it. Both figures come from the belt supplier for your specific carcass, and fabric and steel cord belts differ enormously.
Do I need to allow for splices in the take-up travel?
That depends on whether you intend to re-splice the belt during its life, which is a maintenance decision rather than an arithmetic one. If you do, each splice takes a fixed length of belt out and the take-up has to give it back. The share it represents falls as the conveyor gets longer, which is why the allowance dominates on a short conveyor and disappears on a long one.
Does this tell me if my existing take-up is big enough?
No. It subtracts what you told it you have from what the arithmetic asks for and prints the difference. Adequacy involves the margin your engineer wants, the temperature range the conveyor sees, how the belt has actually behaved so far and whether re-splicing is on the table, and none of that is visible to a length sum.