I’ve written before about running in RPGs, and in D&D in particular. The sprinting rule did make it into Dragon Heresy, so there is that.

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.

Kinematically Speaking

The issue is really that in GURPS, despite perceptions to the contrary[1], 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[2],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.

Parting Shot

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.

Notes

[1] 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.

[2] The math are the basic kinematics equations. If we assume that our starting velocity is zero, and we cover 5 yards in one second

7 thoughts on “A Sprinter’s Lament

  1. I’d be interested to see where you’re going with this; it’s always struck me as wonky that Gigantism made my Minotaur brute into an agile skirmisher.
    Being a giant slab of upper body strength just doesn’t mesh with that, logically.
    Accelerating in a straight line in bursts is very giant Minotaur, running circles around people not so much.

  2. This seems like a solution looking for a problem – conceptually I know it bothers people that you can accelerate to full speed without any run-up or delay, but how often is that a game breaking issue? Or even a game-effecting issue? Especially since it’s common to have PCs loaded up so their overall Move is pretty low in the first place. I wouldn’t institute this as it is additional detail that only makes low-mobility combatants more immobile.

    All of that said, it’s a good approach when dealing directly with running – a sprint contest, characters running to reach something, chasing a vehicle before it accelerates out of reach, etc. Much like how you only bust out fractional Move scores for distance running, not for turn-to-turn movement.

    1. This seems like a solution looking for a problem

      I think I even noted that in my post. The “real worldiness” of this problem has bugged me for a while, not because it’s a problem at the table.

      I did say that not only was accel vs speed not a problem in play, it’s the other way! GURPS characters are frequently rooted in place unless careful care is taken to adventure in formation. Perhaps your groups have learned this lesson, but the ones I play with never have. From that perspective, and since those same folks optimize their characters (move 6-8+ even with encumbrance, everyone seems to be able to fly, etc) around this, cutting down move even a bit takes a bad situation and makes it worse.

      I just realized that by using Accel = Move/2 and Speed = Move (or the base Move as defined as acceleration is half of Basic Speed, and every one gets a level of Enhanced Ground Move as the basic assumption) I could solve the perceived reality problem without writing any new rules.

  3. GURPS’s one-second combat is, when all is said and done, not an actual second. If nothing else, look at the number of words said in a single round (PCs organizing, threats, demands for surrender, bard-song).

    It’s camera time, it’s comics time, it’s make-believe time, and since attacks are far more celebrated than movement, I’m willing to think of “short seconds” for attacks and “long seconds” for movement.

    Realistically, it should probably be harder to breach defenses (in 3e, feints had to cover the job of deceptive attacks, taking twice as long), making fights last longer, making individual attacks less relevant, so moving for 2-3 seconds wouldn’t feel like missing out on much.

    I guess what I’m saying is acceleration should probably be half Move, *except* in combat.

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