But as I was pondering a Pyramid article for GURPS on the way into work this morning, I realized that I was ignoring a potentially easy solution to my problem. Not everyone perceives this as a problem, but I’ve been noodling on it for a while.
The issue is really that in GURPS, despite perceptions to the contrary, combatants are ridiculously mobile. Or, more specifically, the typical person can accelerate from a stop to some maximum speed, and then return to a standstill in one second, covering five yards in the process. They can also sprint five yards in one second, but then stay at that speed from there.
Note that these two things don’t necessarily imply the same thing! If you look at the kinematics equations,and assume that your final velocity is 5yds/sec, and you covered 5yds in the process, then the average acceleration is V^2/2d, or 5*5 / (2 * 5yds) = 2.5 yds/s^2.
If you assume constant acceleration that takes you five yards, then 5 = 1/2 A T^2, or since T = 1sec, A has to equal 10 yds/sec^2. The velocity at the end of that constant acceleration is not 5yds/sec, but 10.
It’s actually the second one that’s more problematic, since your Move is largely considered to be your acceleration if you use the Enhanced Move advantage. If you have Move 5 and Enhanced Move 2, your maximum speed is 20, but it takes you four seconds to get to that speed. Ergo, your Move is your acceleration. But if you could really accelerate that fast, your speed on the turn after you accelerate is much higher than your basic movement allowance provides.
The upshot: Regular GURPS folks accelerate to top speed really fast.
Acceleration and Max Speed
Rah bah bah. Whatever whatever math. Point is that I wonder if we’d have better results if we assume that the typical character can accelerate half their typically calculated Move, and that top speed assumes the normally calculated move. Call that Accel and Vmax to differentiate from normal GURPSy stuff.
So that would mean that Typical Joe would have Accel of 2.5 and max speed 5, so could in one second cover 2 yards, and in two seconds cover 5, after which speed can climb to 6 (sprint bonus). What does that imply for (say) a 100yd dash? Betweeen 17 and 18 seconds.
If we look at this in a different way, and we say that it requires an Accel of 5.66 to provide us with Usain Bolt’s maximum recorded speed of 27.8mph, then applying the above simple rules gives him a 100m dash time of 9.21s. His real-world record is about 9.3 seconds.
Using the normal GURPS rules and a bit of physics, if we allowed a 5yd/s^2 acceleration as “Joe Average” instead of half that, then the typical average GURPS PC does a 100m dash in 10.3 seconds, and only requires a +12% boost in performance to start breaking records. If we do it the proposed way, performance must increase by +124% to reach the same goals, and “more than twice as fast” is properly Olympian.
The practical effect here is to tame instantaneous movement. That will not help the “pinned in place” feel already endemic to GURPS combat. But by breaking up acceleration into several seconds, it provides a bit more differentiation but also verisimilitude in terms of how to model or represent folks. A quick web search suggests that “the fastest among us” can usually sprint at about 16mph, which using real-world results is around a 14s 100m dash, and my model is about 15.25s.
The reason I care is that when one can put a real-world number on things like acceleration, then comparisons to animals and vehicles becomes more rational and on the same playing field, in terms of numbers and results.
Why I care about this even a little bit is left, as they say, as an exercise to the reader.
 Real perceptions. The one-second time scale combined with relative low movement rates in terms of hexes (yards) per second, combined with fairly routine separations between characters on the march, means that a combat can be over by the time the edges of a formation can get to a local fight. Encumbrance penalties on speed exacerbate this observation. So the characters are both impossibly fast and agonizingly slow at the same time. Very zen.
 The math are the basic kinematics equations. If we assume that our starting velocity is zero, and we cover 5 yards in one second