[Battletech] How fast can a Battlemech walk?

Or: “Can a Locust Battlemech really walk 240m in only 10 seconds?”

The answer, perhaps surprisingly, is “no, it can’t” – a Locust (or indeed any battlemech) could run that far in that time… but it is actually physically impossible for it to walk 240m in 10 seconds (at least in gravity similar to Earth’s). To discover why, we must take a rather fascinating scientific journey that sheds some light on something that perhaps many of us take for granted – the mechanics of how we move on two legs! Read on to learn more…

Part 1: Introduction

There are several fast mechs in the 3025 era – and faster ones in other eras such as the Firemoth and Mercury – that have at least 8/12 MP, which means they can walk up to 8 hexes (240m) and run up to 12 hexes (360m) in a single turn (10 seconds). In 3025 these are the Locust, Spider, Ostscout, and Cicada. These mechs can walk faster that many mechs can run, and that didn’t really seem consistent to me – especially since walking mechs had an easier time hitting targets than running mechs despite travelling at the same speed. I’d never really given it any thought before but the more I pondered the more I felt something was amiss here.

As I considered this, I realised there was a much deeper issue – Locusts, Spiders and other light mechs are physically much smaller than heavier mechs. The shortest mechs (often the lightest as well) are about 8m tall (a Locust is 8.87m tall), and the tallest mechs (often the heaviest) are around 15m tall. A hex in Battletech is 30m across and a turn in Battletech is 10 seconds long, so to walk 8 hexes (240m) in one turn (10s) means that a Locust – a 8.87m tall bipedal machine – must be walking at 86.4 kph! Now, I’d imagine most readers are probably thinking “sure, that’s how fast the game says they move” and thinking nothing else of it, but hear me out. Let’s consider a similar situation – a distance of 240m is about 27 times the height of a Locust. Can you walk a distance of 27 times your height in only ten seconds? For me, that’s a distance of about 49 metres, and I sure can’t walk that distance in 10 seconds! You’ll also find that it’s simply impossible – you have to run to be able to cover that distance in that time (and depending on your fitness level it’s entirely possible that you may not even be able to cover it while running). Your legs simply aren’t long enough and can’t move fast enough to be able to cover the required distance in that time just through walking – so wouldn’t this logic apply to a battlemech too? It turns out that there is some rather interesting science that we can dig into to see if this is true. Do note though that while I do have a scientific background, I am by no means a biomechanist (if that’s what they’re called!)- but I think that after researching this post that I’ve understood the relevant concepts, and I’ve done my best to consolidate what I’ve learned and to summarise it here – hopefully I haven’t made any mistakes and I’m sure I’ve made quite a few simplifications, but I’m reasonably confident that my logic is sound and I’m on the right track here!

Part 2: Walking vs Running

First, let’s consider what walking and running actually are, and why they’re different – we can get pretty deep into the kinematics of motion here but I’ll try to keep this simple. Starting right at the beginning, a “gait” or “gait cycle” is “a pattern of limb movements made during locomotion”. Humans and other animals have a “walking gait”, “running gait”, and may have others (“trotting”, “cantering”, “galloping” etc.). For bipeds, a “stride” is “one complete revolution of the gait cycle, beginning at initial ground contact or heel strike and ending when that same foot comes to that same position again to make ground contact again”. A “step” is half of one stride – “one step would be from the time that [one] foot first makes ground contact at heel strike to when [the other] foot makes ground contact at heel strike” (these definitions are taken from marathonhandbook.com [Ref. 1] – references are listed at the end of this post). I’ll mostly be talking about steps specifically here though, just to keep things simple and consistent.

“Walking” is a relatively slow, relaxed (low energy) and stable state of motion where (for bipeds) one foot is always in contact with the ground during a stride. “Running” is a faster state of motion where both feet are off the ground for some time during a stride – running also requires more energy and has a much higher physical impact on the body due to physical stresses on the limbs caused by the feet hitting the ground at higher speeds and springing off again. The key thing here (which should be pretty obvious if you think about it) is that the mechanics of walking and running are different – running isn’t just “walking faster”, the body moves in a very different way when it runs compared to how it moves when walks, as you can see by comparing the Walking Gait and Running Gait images below (if you really want to get into the weeds of the kinematics of walking and running, Cappellini et al. (2006) [Ref. 2] is a good read!). These are by no means the only types of bipedal gait of course – the definition of “jogging” is somewhat fuzzy but it boils down to a “slow run” below about 2.68 m/s (6 mph) where the jogger takes smaller steps than they would if they were running faster, and “sprinting” is very energetic, fast running (usually only sustainable for short periods) where the steps are longer, the legs rise higher above the ground, and the arms swing much more powerfully too (there are others such as “skipping” and “shuffling” but those aren’t relevant to the discussion here).

It is important to note that although Battletech treats them as equivalent, the transition between “walking” and “running” is nothing like the transition from “cruise speed” to “flank speed” for a wheeled/tracked/hover vehicle – all that happens there is that the wheels or treads rotate more quickly to make the vehicle travel across the ground faster, but the vehicle moves in fundamentally the same way. By contrast, something that moves on legs has to change from a walking gait to a running gait as it accelerates, which requires a significant change in how it moves, its stability and in the stresses applied to its limbs while in motion.

Part 3: The Froude Number – a physical limit to walking speed

A human’s walking speed depends on their height (or more specifically, the length of their leg), distance between steps, number of steps taken per second (“cadence“), and various other factors – generally speaking an adult human’s step length will range from about 0.64m to 0.82m [see Ref. 1]. It turns out that as walking speed increases, there comes a specific point known as the Walk-Run Transition (WRT) around which humans (and other creatures) invariably prefer to switch to running rather than to continue walking.

To explain why, we have to introduce the Froude number. The Froude number has a rather fascinating history that is summarised very well in Vaughan & O’Malley (2005) [Ref. 5], which explains how it started out as a concept in fluid dynamics which found an application in modelling resistance in naval ship hulls with different sizes, and was then adapted to bipedal locomotion. The Froude number (Fr) is calculated by a simple formula:

Fr = V²/gL

where V is the forward horizontal velocity of the biped in m/s, g is the gravitational acceleration in m/s² (9.81 on Earth), and L is the length of the biped’s leg (height of the hip above ground) in metres.

Its derivation is explained in Usherwood (2005) [Ref. 6], but suffice it to say that in locomotion studies the leg can be considered to be an “inverted pendulum” rotating around the foot on the ground (this is an approximation, but it happens to be a pretty good one), and the Froude number is the ratio of the centripetal force of the leg moving around the foot to the force of gravity acting on the body. The Froude number can be used as an equivalent to the biped’s speed – higher Fr numbers mean the biped is travelling faster. Interestingly walking actually becomes physically impossible when the centripetal and gravitational forces are equal at Fr=1.00, because beyond this point the feet can no longer remain in contact with the ground during the step cycle – this means that the biped HAS to be running to maintain its motion (this happens around 2.97 m/s (10.7 kph) for an adult human). However, the previously described Walk-Run Transition (WRT) actually happens at a lower speed than this – around Fr=0.5 – and this is consistent not only among humans but among many other animals too. The biped wants to start running when it reaches Fr=0.5, even though there is no actual physical requirement to do so – one possible reason suggested in Usherwood (2005) is that above Fr=0.5 the swinging leg cannot move fast enough to maintain a walking pace without significantly more active effort, so attempting to do so would be “too costly” and inefficient (this was borne out by my own observations on the treadmill, described below).

Part 4: How humans walk, run and sprint

The chart above shows the Froude numbers and corresponding speeds for an adult human with a leg length of 0.9 m. I’ll go over these in more detail below – in the name of “SCIENCE!” I also went down to the local gym and tried as many of these as I could on a treadmill to get a feel for how fast these were, so I’ll add my observations as a reasonably healthy 1.8m tall, 82 kg, almost 50 year old adult human male:

Fr=0.25: Optimal walking speed – this is supposedly the speed at which most people prefer to walk, considered to be around 1.4-1.5 m/s. I think I would describe this more as a “purposeful stride” at around 120 steps/minute – a more relaxed “pottering around the house” walking speed would be more like Fr=0.15 (1.15 m/s, or 100 steps/minute) – but it’s still a fairly realistic walking pace if you’re trying to get somewhere.

Fr~0.50: “Walk-Run Transition” (WRT) – The Walk-Run Transition starts to kick in around Fr=0.50 (2.1 m/s) – I could still walk (quickly) at this speed but it was difficult, and I was taking about 146 steps/minute. I actually found that I could keep walking up to around Fr=0.70 (2.49 m/s, about 170 steps/min) but my legs were really straining to keep that pace, and I really wanted to switch to a jog which would have been much easier to maintain. I had been slowly incrementing the treadmill speed by increments of 0.1 mph (0.045 m/s), and apparently this makes it easier to maintain a walking gait at higher speeds than if it was being incremented in larger steps, so still being able to walk (with difficulty!) a bit beyond the calculated WRT isn’t unexpected. However, it was just too difficult for me to keep walking above this speed.

Fr=0.80: “Fast Jogging” – By the time I hit Fr=0.80 (2.66 m/s) I was jogging at 182 steps/minute and it felt like I was taking smaller strides than my very fast walk at Fr=0.7, but it felt much more comfortable – this is considered a fast jogging pace and much faster than this would be considered “running” rather than “jogging”.

Fr=1.00: “Max Walk” – At Fr=1.00 (2.97 m/s) I definitely had no hope of maintaining any kind of walking gait and I was firmly in the running regime, taking bigger strides than previously and running at 184 steps/minute. It should be noted that human “race-walkers” can apparently walk significantly faster than Fr=0.50, but they have to physically change their walking style (usually moving the hips a lot more) – however, whether they’re actually “walking” at this speed is debatable since slow-motion video playback of competitive race-walks clearly shows that they often have both of their feet off the ground at the same time, which would therefore mean they’re running!

Fr=1.50: “5k run pace” – The fastest speed I could reach on the treadmill during my data-gathering session (I’ve been very out of practice when it comes to physical exercise!) was Fr=1.45 (3.58 m/s), which was a pretty fast run that I couldn’t maintain for much longer than a minute – I was taking around 204 steps/minute which is rather high, apparently it’s better to aim for a cadence of 180 steps/min. Just above this level (at Fr=1.50) is consistent with a good amateur time for a 5k run (about 23 mins – the world record is much faster at 12 mins 35 secs!). I’m pretty sure that with more discipline and training I’d be able to run at this pace more efficiently and for longer, but this was as fast as I could run in my treadmill session and it felt very strenuous!

Fr=2.50: “400m sprint” – This would be considered a fast run or sprint at 4.7 m/s, and represents a reasonable amateur time to complete a 400m race (85 seconds, again a far cry from the record time of 43.03 seconds!). At this point a human would be running at just over 10 miles per hour.

Fr=5.00: “100m sprint” – This represents a good amateur time for a 100m sprint (about 15 seconds) and would definitely be considered to be “sprinting” rather than “running”.

Fr=12.345: “Usain Bolt avg 100m” – This corresponds to Usain Bolt’s average speed during his record-setting run at the Men’s IAAF 100m sprint finals in 2009 (10.44 m/s). This marks the current limit of human capability and such speeds can only be maintained for a short time.

Fr=17.472: “Usain Bolt max 100m” – This represents Usain Bolt’s absolute maximum speed measured during that race (12.42 m/s).

Faster speeds for humans may be theoretically possible, but if so nobody has attained those yet!

The Froude number is important for our purposes here because it can be used to describe a state of motion that is consistent across all scales – whether we’re talking about a fictional tiny Lilliputian, a small child, a tall adult human, an ostrich, a tyrannosaur, or a giant bipedal battlemech – but the specific speed at which they’d be moving to achieve those Fr numbers would obviously be different because the leg lengths would vary with height too. Thus, the optimal walking speed for all of those bipeds occurs around Fr=0.25, the WRT for all of those occurs around Fr~0.5, it is physically impossible for any of them to walk faster than the speed corresponding to Fr=1.0, and all of them would be running (or sprinting) at higher Froude numbers!

Which brings us, finally, to Battlemechs…!

Part 5: So how fast can a Locust walk?

The table below shows the leg lengths for some well-known mechs, along with their maximum stated walking speeds in kph taken from their Technical Readouts (1 MP = 10.8 kph). Since most mechs generally have human proportions, their leg lengths are assumed here to be 0.5 times the total height of the Mech. The Locust and Cicada are assumed to have longer legs that are mounted higher up on their profile (the Locust’s full height is actually 8.87m, and a Cicada’s full height is assumed to be 11m), though this seems to have changed in more recent artwork which presents the Locust with legs closer to its mid-height – but let’s assume that they retain the longer legs here. The heights used to calculate the leg lengths were mostly taken from the Battlemech Scale Chart (and other semi-official sources where possible).

Now if we plot these values on a graph showing speed vs leg length, the results are rather interesting!

The coloured lines on this graph mark the transitions between different types of gait (in earth-like 1g gravity). As speed increases for a given leg length, the biped will transition from walking to jogging to running to sprinting (corresponding to the Froude numbers defined above), and bipeds with longer legs will change to faster gaits at higher speeds than those with shorter legs. The key thing to understand is that anything above the green Fr=1.0 line is some kind of run – close to this line is a “fast jog”, the pink line is a “fast run”, the purple line is a “sprint”, the blue line is a “fast sprint”, and the orange line can be considered the “maximum sprint”. In practical terms, the blue Fr=5.0 line should be considered to be the fastest that battlemechs can reasonably reach in a battlefield situation – but remember that mechs are sprinting at this point and are therefore already pushing their locomotive systems to the extreme. I would suggest that the orange (Fr=12.345) line equivalent to Usain Bolt represents the absolute maximum speed that a mech specifically designed for racing could reach in ideal conditions (e.g. a speed record attempt on something like a salt flat). I think it is reasonable to assume that this kind of speed would be unattainable in the chaotic, variable battlefield environment (and it would be extremely dangerous to attempt to do so).

Now (finally!) we can answer our initial question – “can a Locust really walk 240m in only 10 seconds“? From the graph above we can see that the answer is “no, it cannot!“. To move at a speed of 86.4 kph puts a Locust far above the green Fr=1.0 line on the graph that represents the maximum possible walking speed for even a 7m leg length, and actually puts it well above the blue Fr=5.0 line equivalent to a 100m sprint – so it would have to be sprinting (at dangerously high speeds) to move this fast! Another surprise is that speed corresponding to the Fr~0.5 walk-run transition (red line) for the Locust is only 21 kph, and the speed at which it can no longer use a walking gait (Fr=1.0) is only about 30 kph. So in reality, a Locust could only walk at most three hexes per turn (3 MP), and to move faster it would have to run in some way (and it would have to sprint to move 8 hexes in 10 seconds). It would actually have to go beyond the “max sprint” (Fr=12.345) line to run at its stated maximum speed of 129.6 kph (12 MP), which would be impossible on a battlefield (if not anywhere else too)! Therefore, it is impossible for a Locust to walk at 86.4 kph (though it is quite capable of running at that speed)!

You can also see the difference that the leg length makes when you look at the Spider – this humanoid mech has much shorter legs and is practically at the orange “max sprint” line at its maximum stated “walking” speed, whereas the longer-legged Locust is well below that line (though still quite far above its “100m sprint” line) – if the Locust did have shorter legs that were half its height then it would actually be above the “max sprint” line at 8 MP too. Like the Locust, the Spider wouldn’t even be able to “run” at 12 MP because that is far above the orange line and therefore well into the “possibly only achievable in ideal racing conditions” region. The shorter Star League era Mercury mech is just beyond the “max sprint” line at its stated 8 MP walking speed too, and the Clan Firemoth (Dasher) mech is even further above it with its 10 “Walk” MP!

What happens around Fr=0.5 for battlemechs depends on how we interpret the WRT at Fr~0.5 – does that represent a hard limit or is it something that a mechanical body could be designed to ‘power through’ or work around so they can still walk (rapidly) right up to Fr=1.0? My own experience has shown that Fr=0.5 isn’t a hard barrier beyond which walking is impossible, but it certainly becomes more difficult, more tiring, and less comfortable to walk faster than that, and it doesn’t feel like a stable way to move since I had a very strong urge to flip between walking and jogging in that regime. That said, Battlemechs would not “tire” as humans do, though their joints and myomer “muscles” could still be over-stressed in extreme situations. Personally I would say that a Battlemech could continue to walk (quickly) between Fr=0.5 and Fr=1.0 since it could be designed with mechanical and gyroscopic aids that are unavailable to organic bipeds, but it is still impossible for a battlemech to walk beyond Fr=1.0 since this is marked by a physical limit.

If we look at the slower end of the speed scale, we can see that the massive Annihilator is the only mech on the graph that can truly walk at its stated walking MP of 21.6 kph (2 MP), since that is just below the red Fr=0.5 line – it would actually be “jogging” at its run speed of 32.4 kph since that would be just above the Fr=1.0 line. The Urbanmech on the other hand has much smaller legs, which place it between the red Fr=0.5 line and the green Fr=1.0 line at 21.6 kph, so they would be walking normally at 1 MP, “fast walking” at 2 MP, and properly running at 3 MP. The Atlas’s stated walking MP (3/5) would have it jogging at 32.4 kph and sprinting at 54 kph. Mechs with higher stated walking MPs would at the very least be running if not sprinting at those speeds.

Part 6: What does this mean for Battletech?

Battletech is a game centred on 8-15 metre tall death-spewing bipedal war machines that weigh between 20 and 100 tons that stomp around at high speeds over all sorts of terrain, and some of them can even jump hundreds of metres horizontally through the air (and dozens of metres vertically!) – so there’s plenty about it that isn’t particularly realistic, and “fixing” one of its less realistic aspects isn’t going to fix the rest! I may have just demonstrated that the way that battlemechs move in the game isn’t realistic, but I’m certainly not arguing that everyone should throw out their games or change how they play – the game is fun as it is and it’s fine to leave it like that! The reason I went as far as I did down this scientific rabbit-hole was more out of scientific curiosity and hopefully (if you’ve stuck with the article this far) you’ve found it interesting too and have learned something along the way as I did – personally, I think it’s rather fascinating to know that there’s a speed beyond which we’d really prefer not to walk (and a speed beyond which we literally cannot walk). So by all means, continue to play Battletech as you always have!

That said… I’m very much a rules tinkerer, and there’s a lot about Battletech’s movement system that think could be improved. I’m fairly confident that what I’ve described here could be implemented as optional “Advanced Rules“, and now I have a base to build something from – and there are already (Advanced) rules for Sprinting in the game that could be modified and applied to simulate what I’ve described here. I also think that a more realistic system could allow players to use more interesting tactics than the current movement system can accommodate. Mechs would now have similar walking speeds (2-3 MP), a range of MP above that where they would be running, and if they can move fast enough a sprinting range above that – this would affect firing modifiers for combat too. Since walking would now be consistent for all mechs, the desired running speed would be used to define how many MP the mech could move during mech design. There would be a hard limit to the maximum speed at which a mech could travel – MASC, Superchargers and other speed-enhancing technology would be much more limited (and more dangerous). Since mechs wouldn’t be able to fire weapons while sprinting, that would also restrict what I consider to be the very “gamey” tactic of attempting to get behind a target to open fire on their more vulnerable rear armour. I’m sure it would play differently from the default Battletech rules but I think it could be a lot more interesting as a result too. But I’ll go into more details about these ideas in another post – I think this one has gone on for long enough!

Thanks for reading, and do let me know if you have any thoughts, comments or questions!

References
[1] – https://marathonhandbook.com/average-stride-length/
[2] – Cappellini et al. (2006), “Motor Patterns in Human Walking and Running”, J Neurophysiol 95: 3426–3437 ; https://journals.physiology.org/doi/full/10.1152/jn.00081.2006
[3] – Perry J., Burnfield J. M. (2010). Gait Analysis: Normal and Pathological Function. New York, NY: Slack Inc.
[4] – https://www.msahc.com.au/news/3d-gait-analysis-to-identify-running-injury-risk
[5] – Vaughan & O’Malley (2005), “Froude and the contribution of naval architecture to our understanding of bipedal locomotion”, Gait and Posture 21, 350-365 ; https://me.queensu.ca/People/Deluzio/JAM/files/04.01.2011_Kevin.pdf
[6] – Usherwood (2005),”Why not walk faster?”, Biol Lett. Sep 22; 1(3): 338–341 ; https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1617162/