The flying bike is a mostly real thing. Mostly in that it actually flies - but not with a real person. Here is the developer's site (Duratec) and a good review from Mashable where they add that the whole thing weighs 209 pounds. The claim is that the bike can not yet support the full mass of a real human and the demonstration only ran for 5 minutes.
You probably know what comes next, right? Now I will make an estimate of the battery size for this thing to actually work. And by "actually work", I mean that it should be able to carry a normal adult for at least 30 minutes. I mean, who would want a flying bike that only runs for 5 minutes?
How Does a Hover Bike Fly?
Let's think about this in terms of basic physics. The bike doesn't fly because of fairy dust. No, it flies because it is "throwing" air down. The blades take stationary air above the bike and push it down. Since the bike is pushing air down, the air pushes back up on the bike. If the force from the air on the bike has the same magnitude as gravitational force on the bike, it will hover (stay stationary in the air). Simple right?
How about diagram? I already looked at the physics of hovering when I calculated the power needed for the human powered helicopter, so I will just start with that image.
Here you can see what matters when dealing with helicopter thrust. You get the greatest thrust force when you have the largest change in momentum of air. If you assume the density of air is constant, then there are two important parameters: the speed of the air and the size of the rotors. I will skip over the derivation (but you can find it here), but there are really just two important equations.
First, there is the power required to hover.
In this expression, ρ is the density of the air, A is the area of the rotor and v is the speed of the air coming out of the rotors. I can find this thrust air speed by looking at the weight of the aircraft and the change in momentum of the air. I get:
Well, what if I don't know the thrust speed of the air? No problem. I just solve for the thrust speed from the force equation and plug it into the power equation.
And there you have it. The power needed to fly depends on the mass of the object and the area of the rotors. This is why the Gamera II human powered helicopter has such a large rotor area. Actually, this is wrong. It is just a little bit wrong since it assumes a perfectly efficient system. However, I can make a nice approximation of the actual efficiency by looking at some real helicopters.
This is a plot of calculated power (with efficiency) vs. listed power for some helicopters on Wikipedia - just like I did before with the S.H.I.E.L.D. Helicarrier. If I adjust the efficiency to 40%, then I can get a nice slope value of 1.
There are two problems with this model. First, I am going to use this for much smaller masses - like the hover bike. Second, the listed power is the maximum engine power (I assume). I wouldn't think you would need maximum power to hover. If I had to guess, I would say somewhere around 50% power but I really don't know. Of course neither of these things will stop me from moving on (nothing ever does).
Battery Energy and Mass
What kind of battery would you like to use for this hover bike? It has to have a high energy mass density. If you add some big old lead-acid batteries, you are going to have a weight problem. Wikipedia's page on energy density lists the lithium-ion battery with an energy density of about 0.8 MJ/kg. I will just assume 100% efficient batteries. That means that if I know the required power for my device, I can calculate the mass of the batteries (which will of course change the required power).
In this expression, Δt is the flight time and dE is the energy density.
Estimating the Battery Mass
So, I have an expression for the mass of the battery based on the power. I also have an expression for the power that depends on the mass (total mass). Let me write the hover bike power based on the mass of the battery and the power based on the rotor size as:
With a few estimates, I can plot the power vs. battery mass for the two functions. When they intersect, I have my mass. Simple really. Here are my estimates.
- Rotor size: There are two big rotors with a radius of about 0.5 meters and two smaller ones with a radius of maybe 0.3 meters. This would put the total rotor area at 2.14 m2.
- Bike + person mass (called mo in the equation). Without the batteries and a full sized human, I am going to guess 140 kg.
- Time of flight - 30 minutes or 1,800 seconds.
- Efficiency. Even though I took the time to estimate the efficiency, I am going to leave it off. Why? Because this will be balanced by the fact that the motors won't be at full throttle all the time.
- Density of air = 1.2 kg/m3.
- Energy density = 0.8 MJ/kg.
And now for the plot of the two functions.
These two functions intersect at a battery mass of 151 kg (333 pounds) and a total motor power of 67.5 kilowatts. That mass is about half the total hover bike mass and the power is pretty high too. There is one more thing to calculate - the thrust speed. For real helicopters, I estimated the speed of the air at about 25 m/s regardless of size. Using the same formula, this hover bike would have a thrust air speed of 47 m/s. I'm not saying you can't do that. I'm just saying that real helicopters have lower thrust speed. That's all I'm saying.
There is one way to make this possibly work. What if you wanted a flight time of only 15 minutes? In that case you wouldn't need as large of a battery so you wouldn't need as much power. This means that a battery half the mass of the 30 minute one would be too much. If you run the calculation for a time of 15 minutes, you only a battery mass of 35.6 kg (78 pounds). That seems more reasonable for a battery mass - but maybe not so reasonable for a functioning flying bike.
If you only had a five minute flight time, the battery would be even smaller. I guess this is why the vehicle has bike wheels. You will likely have to ride around as a bike for most of your travels. Of course there is another way to fix this vehicle - make rotors with a much larger area (which requires lower power). But if the rotors got too big, you might not call this a hover bike. In that case you would probably call it an electric helicopter.
