Rate of rise (RoR): reading the line under your roast curve
The temperature curve tells you where the roast is. The rate of rise tells you how it got there and where it is heading. It's the slope of the temperature line, in degrees per minute, and once you can read it you'll spot problems a minute or two before you'd taste them.
What it looks like
Right after the charge the beans are cold and the drum is hot, so they heat fast. The line starts high and slides down as the beans warm up and approach the drum's own temperature. That slide is what you want: smooth, always heading down, never jumping.
You'll often see the rate of rise a bit noisy on a real log, because a probe in a moving bean mass jitters. Look at the shape over a minute or two, not at single points.
The two shapes to be afraid of
The crash. The line drops off a cliff, often around first crack, and the roast nearly stops. This usually comes from cutting the heat too hard, or from the coffee itself cooling as the water in it flashes to steam. A stalled roast tastes flat, baked, a bit like cardboard.
The flick. The opposite: the line turns around and heads up near the end. It happens when the roast has slowed to a crawl, someone adds heat, and the beans suddenly get an energy boost they can't use well. A flick tends to give a roasty, scorched edge and sometimes tipping, where the ends of the bean darken.
Both come down to the same idea: you want to steer gently and early rather than slam things late.
What to do about it
If the line is running high through the middle of the roast, you're going to arrive at first crack fast and short on development. Lower the gas a bit, a little earlier than you think.
If it's falling too fast before first crack, you've got too little heat going in. Give it a touch more, or check your airflow isn't pulling all the heat out of the drum.
Make one change at a time, note it, and see what the line does next time. It's slower than flipping three dials and hoping, but you end up with something you can repeat.
A note on numbers
People quote specific RoR values at first crack. They depend on the batch size, probe and software smoothing. We'd rather you learn your machine's normal shape from a dozen logs than aim at someone else's figure. Once you have that, deviations stand out immediately.