Some time ago I made an attempt to answer the age old question: How fast is Sonic the Hedgehog? based entirely on evidence from that spiky fiend’s first outing on Sega Mega Drive. I’ve decided to revisit the theme, but today I’m going to take the magnifying glass to the disturbingly common item in the Sonic-verse; Springs.
Anyone with even a passing knowledge of Sega’s wayward mascot will know that he can use the liberally placed springs to propel himself skyward and that in the first game (which is what we’re working from here) they came in two flavours: Yellow & Red. The latter being a turbo charged version for special occasions and the former the average spring for day-to-day bouncing. To keep everything extreme and with sufficient …erm… attitude… to do justice to the “fastest thing alive” I’ll be focusing on the red springs.
What Exactly Are the Springs?
Before I get on to what they are, I need to be clear on what they’re not. They are NOT bouncy trampoline-type items; Sonic doesn’t need to apply force downwards in to them in order to be propelled back upwards. Instead the spring can be activated just by touching the platform; either by stepping, falling, or jumping on to it. Once activated the platform shoots upwards a small amount and propels Sonic a consistent height in to the air (I’m assuming the traditional floor mounted springs here).
Upon activation the uncoiled spring can clearly be seen below the platform before it snaps back to its resting state.
The only seemingly rational conclusion is that the springs are much more complex than they initially appear: In their resting state the spring is held in compression and the upper surface must double as some kind of pressure plate (either electrical or mechanical) and launching platform. When activated the spring is released and the stored potential energy is spent throwing Sonic up in to the air. In almost the same time as it takes the spring to uncoil it is immediately re-compressed back to its resting state ready to fire again suggesting some high powered actuator/motor embedded below the surface.
How Fast is Fast? and how Powerful is Powerful?
In order to get a better understanding of the engineering at work here I need to start putting some numbers to the Sonic/Spring situation. Luckily (as before) Sonic is a convenient measurement of unit himself with an official height of 1 metre and weight of 35 kg.
… it is kind of lucky that he has an official weight because I was intending on looking up average weights and lengths of hedgehogs and extrapolating for Sonic’s height; I kind of feel like that might have been a rabbit-hole…
From this, and a hastily compiled example from Spring Yard Zone, I found that the spring “unfurls” 0.43 m in propelling Sonic upwards and from that point he flies a further 14.4 m in to the air…. check out the picture below to see what I mean…
… I also found out that it takes approximately 0.07s for the spring to return to its resting state which will be important later.
Note on assumptions: For the purposes of this I’m going to assume earth’s gravity. I’m also assuming negligible mass to the launch platform itself and no wind resistance because I couldn’t get approval for wind-tunnel time in order to pop a hedgehog in to the working section.
In order to propel Sonic that distance in to the air we can use constant acceleration formulae, specifically:
v^2 = u^2 + 2ax
Substitute in the known values and we can find that upon leaving the spring Sonic is travelling 16.8 m/s (or 37.6 mph) … incidentally this is much faster than he can run…
Ok, so that’s not too crazy; I mean, yeah under normal circumstances a hedgehog travelling at just under 40 mph vertically upwards would raise some eyebrows, but this is Sonic – it all sounds pretty tame.
The energy required to do this is equal to the gravitational potential energy that Sonic has at the top of his flight (PE = mgh). Again substituting the known vales gives an energy input from the spring of 4944 J and by substituting in to the formula for energy stored within a spring (knowing that the spring extended by 0.43 m during hedgehog launch):
PE = (1/2)kx^2
We can find that the Red Spring constant, k = 53478 N/m which at the start of the launch (compressed by 0.43 m) will exert 23 kN upwards on Sonic… which means that at the moment the spring is activated, Sonic will accelerate at 657 m/s^2 …
… or around 67 g …
To put that in context, John Stapp was a pioneer of the study of acceleration and deceleration on humans. He is credited with experiencing the highest g-force ever voluntarily by a human (and surviving) in his rocket sled experiments at 46.2 g.
And he doesn’t even seem to bend his legs to adsorb the shock! He really is the hedgehog with attitude!
… but let’s not forget the engineering marvel that is the spring itself. Not only can it blast Sonic upwards with a monumental acceleration over its incredibly short travel distance, it also manages to reset in 0.07s which equates to a motor with power of 70.6 kW or 95 horsepower all hidden somewhere in the base of that inconspicuous commonplace ingame item.
Anywho, next time you bounce on one of those ingame springs, just take a moment to appreciate the engineering involved and Sonic’s poor skeletal system being battered by that acceleration…
Note: The above piece was written to entertain and I made many assumptions and simplifications for these purposes…