Yesterday Todd Reichert went 139.45 km/h - 86.65 mph - using nothing but his muscles.
Some people claim Usain Bolt holds the title with his 9.58 second 100 meter world record sprint.1 An amazing run with a peak speed of 43.92 km/hr, but humans are terrible sprinters compared to more than a few land animals like cheetahs. We're really good at the longer distances, so perhaps it makes more sense to consider milers or longer races more representative of human achievement.
I'd argue the fastest person is the one who goes the fastest on muscle power. It may not be pure to consider a cyclist, but cycling is much more efficient than running.
Most of the power required to travel at high speeds goes into moving air out of the way. A few years ago I posted a simple back of the envelope derivation showing the power required to cut through the air increases as the cube of velocity. On a normal bicycle you start to feel strong wind resistance around 15 mph and you're working very hard at 20mph. You can make your life easier by improving your vehicle's aerodynamics. Road racing cyclists spend thousands of dollars making slight improvements to their bicycles.
A person on a bike isn't the most aerodynamic object. The equation I derived is sensitive to the area of the air column you travel through. This turns out to the the cross section frontal area of the moving object times a coefficient of drag - a term that depends strongly on the shape of the object. A Tour de France racer in a racing tuck has a coefficient of drag, a Cd, of about 0.7 and presents a cross section of about 0.5 square meters to the wind. Someone riding a casual commuter bike has a larger Cd and cross sectional area. They effectively travel through a larger tube of air, but at a much lower speed.
Velomobiles are streamlined bicycles. They're rarely seen in the US - perhaps a few thousand have been made and mostly in Germany and the Netherlands. Commercial models have frontal areas similar to that of a cyclist, but the Cd is usually in the 0.1 to 0.15 range - tiny by the standard of even the most aerodynamic cars.2 Even though they're larger and heavier than a regular bicycle, it is relatively easy for a normal rider to cruise along at 25 mph.
The Aerovelo Eta Todd Reichert piloted is the part of a serious engineering project involving some University of Toronto people. The Eta's frontal area is 0.35 m2 and its Cd is an astounding 0.038. A bit of calculating shows the Eta should be nearly three times as fast as a Tour de France road bike at speed with the same power input.3
One hundred miles per hour on a bike is a magic number. Although Todd is an excellent athlete, he isn't in the elite class. Just to move the air you need (161/140)3 times as much power. 100 mph on 1.5 horsepower - perhaps within the reach of an elite cyclist.4
From an old post Colleen delivers an easy 100 watts of power to the pedals of her bike at about 14 mph. That works out to about 1,025 mpg if you use the energy equivalent of vegetable oil and it goes up dramatically with a velomobile.5 Her speed improvement in the Eta would be something close to a factor of two. She should easily be able to cruise at nearly 30 mph and easily sprint to 40. Her power output is well within the capability of many commuters.
It seems very wasteful to have 3,500 pounds or more of car dedicated to move less than ten percent of that weight most of the time. Velomobiles operating in a 30 to 40 mph range would be great for 15 mile commutes and would be readily be adaptable to electrification. In mass production a practical version would probably sell for under $2,000. Unfortunately a problem that comes up whenever you start thinking about elements of a system rather than the full system. The velomobile, car, bus, or whatever is part of a very complex and expensive system that took decades to build and partly defines how we live. Massive systems have a lot of inertia.
1 A fascinating paper looking at the physics of the run. His peak speed was 12.2 meters per second - about 27mph. Peak acceleration came out of the starting blocks at 9.5m/s2 - 0.97g and peak power came a second into the run at 2.6 kW - nearly 3.5 horsepower. His body had to somehow deal with over 10,000 watts of excess heat at the time.
On the performance of Usain Bolt in the 100 m sprint
J J Hernández Gómez, V Marquina and R W Gómez
Published 25 July 2013 European Journal of Physics, Volume 34, Number 5
Many university texts on mechanics consider the effect of air drag force, using the slowing down of a parachute as an example. Very few discuss what happens when the drag force is proportional to both u and u2. In this paper we deal with a real problem to illustrate the effect of both terms on the speed of a runner: a theoretical model of the world-record 100 m sprint of Usain Bolt during the 2009 World Championships in Berlin is developed, assuming a drag force proportional to u and to u2. The resulting equation of motion is solved and fitted to the experimental data obtained from the International Association of Athletics Federations, which recorded Bolt's position with a laser velocity guard device. It is worth noting that our model works only for short sprints.
2 a few Cd numbers for reference:
0.7 - 1.1 F1 car - very unaerodynamic and variable depending on downforce
0.7 Lotus Seven
0.6 - 0.8 normal semi truck (this is very low hanging fruit)
0.51 Citroën 2CV
0.48 VW Beetle
0.38 VW New Beetle
0.37 Ferrari F50
0.32 Honda Accord Coupe 2002
0.32 VW GTI Mk V 2006
- most current production sedans are in the 0.31 to 0.33 range
0.31 Audi A3 2014
0.28 Chevy Volt
0.275 Ford Fusion 2013
0.27 VW Golf Mk7 2012
0.25 Toyota Prius 2010
0.24 Mercedes S & C Class 2014
0.24 Tesla Model S
- dropping below 0.24 and still looking like a car is very difficult
0.195 GM EV 1
0.189 VW XL1 2015 ('production')
3 The back of the envelope:
Tour de France road bike Cd with rider is 0.7 - 1.0, area ~ 0.5 m2
Aerovelo Eta Cd = 0.038, area = 0.325 m
F~ 0.5DCdAv2, P = Fv → P ~0.5DCdAv3 (D is air density)
for the same power CdAvn3 = CdAve3
assume n is normal road racing bike with CdA = 0.7 * 0.5 and e is the eta with CdA = 0.038*0.325
0.35vn3 = 0.0124ve3
ve/vn ~ 3 ... everything else being equal (power, transmission efficiency, wheel friction, ...), the Eta should be about three times as fast as a normal optimized road bike. It should be noted that over 90% of the power going into a road bike at speed pushes air out of the way.
4 Some rough numbers on how much power can be supplied over time. Elite male athletes are not shown. A TdF rider can usually supply about 6 watts/kg of body mass for thirty minutes or so. These guys are usually light and all leg muscle, so we're talking about 400 watts. Sprinters can easily go over 1,000 watts for short periods. 1,100 watts might move the Eta past 100 mph including sources of drag other than wind resistance.
5 In theory this would work - vegetable oil has the same energy density as diesel fuel, but people prefer regular foods. One of those comparison -only-don't-try-this-at-home numbers. Colleen on her bike has a Cd of 0.91 and a frontal area of 0.72 m2. An upright riding position and a very tall rider. The speed increase can be found by equating the power required by her bike and the Eta: 0.66vn3 = 0.0124ve3 → ve/vn ~ 3.7 assuming it is dominated by wind resistance. That is only the wind resistance component. Since we're not at extreme speeds the overall speed improvement is less. Another back of the envelope that I don't show suggested it is reasonable to expect an improvement by factor of 3 resulting in a cruising speed of a bit over 40 mph. Effective mpg would be in the 3,000 mpg range.
A commuter velomobile would have to be larger than the Eta to accommodate larger drivers and baggage. The frontal area would be larger and the Cd is unlikely to be as optimized as it would need better interior ventilation among other things. Even so a Cd of under 0.1 should be easy along with a frontal area of 0.5 m2. That would give a speed improvement of 2.3 on wind resistance and at least 2 overall. So she would be traveling close to 30 mph on the same effort she currently uses. Longer trips, higher speeds and better hill capability could be had with small auxiliary electric motors making it a human-electric hybrid.
No recipe this time, just a link to a new tomato - the Rutgers 2.0 to celebrate Rutger's 250 anniversary. Sign me up, I look forward to getting some seeds to grow next year.