Analysis of a flywheel's potential!

A flywheel is a device that stores kinetic energy in the form of a mass rotating at very high speeds. Imagining that you'd want the device to be "tubular"(so it can be readily attached to the bike) or be cylindrical in some form, we could use the formula for kinetic energy for a rotating mass. Let's the define the height of the cylinder as H, the radius as R, the mass of the cylinder as M, the moment of inertia being I, and the angular velocity being W. Since the highest moment of inertia would be found with a completely filled cylinder, it'll be a solid cylinder for modeling purposes.

The formula for moment of inertia is...
M = density*volume = pi*R^2*H*density
I = M*R^2/2 = pi*R^4*H*density/2 ; http://en.wikipedia.org/wiki/List_of_moments_of_inertia
Kinetic Energy(K_E) = 1/2*I*W^2 = pi*R^4*W^2*H*density/4 ; http://hyperphysics.phy-astr.gsu.edu/Hbase/rke.html

From this, we can directly calculate the kinetic energy of the fly-wheel just knowing the height(meters), radius(meters), angular velocity(radians/sec) and density of the material(kg/m^3)! And it'll be in joules, so to compare it to a li-on battery, you'd use the calculation Ah*Voltage*3600 for the battery(The battery has 3600*Ah*Voltage joules, roughly).

So, let's take some reasonable values. As you can see, the flywheel energy is to the fourth power of the cylinder's radius so you'd want to maximize that as much possible! But... where to put a fatty cylinder on a bike, eh? :lol: Let's assume you bring your trailer along behind the bike and using gears and clutches, you can extract energy from the wheel when necessary. Let's say the radius is 1m, the angular velocity is 20,000 RPM or 2094 radians/sec as http://www.convertunits.com/from/RPM/to/radian/second says so, the height is 1 meter and the density of the material as found at http://en.wikipedia.org/wiki/Density#Density_of_composite_material for lead is 11,340 kg/m^3 and the final kinetic energy is *crunching*...

pi*R^4*W^2*H*density/4 ~= 3.14*1^4*2094^2*11,340 =

3.9 x 10^10 Joules. For comparison, a 72volt, 20 Ah battery has 72*20*3600 joules or
5.2 x 10 ^6 joules meaning the flyweight stores 10000 times as much energy. The drawback? Can you imagine the weight of this imaginary fly-wheel? Let's calculate... pi*R^2*H*density ~= 3.14*1^2*1*11,340 = 35607 kg which is only about 39 tons or about 78,500 lbs! Ok, so let's reduce that weight to the weight of a 72 volt 20Ah battery by only reducing the height(so that the reduction in stored energy is minimized as it's only linear to kinetic energy)... I assume the battery is about 30 pounds so reducing the height by about 78500/30 times or about 2616 times, we get a flywheel that's about 4 times more energy dense than the lithium ion battery at the same weight. The major problems in achieving this, however, is the mechanical complications of converting the rotational energy of the fly-wheel to the drive-system, minimizing the resistive losses of the rotating fly-wheel so it won't be slowed by its own friction, and getting a large enough radius to be meaningful but yet a low enough height where the weight won't be so burdening while also ensuring the cylinder's structural integrity. Getting even higher sustainable angular velocities would also help quite a bit... increasing the angular velocity by 5 times would increase the amount of stored energy by 25 times! But... 100,000 RPM sounds like it's entering the realm of the bleeding edge.

You mentioned the weight...but the angular momentum would be nightmarish for bicycle handling.

Following the wisdom of Bosch...

How about this:

You have an independent Switched Reluctance Motor flywheel that is setup onto the front wheel with a freewheel and clutch mechanism. The act of using the brakes (pulling on the brake lever) engages the clutch (which does waste some energy in friction) and transfers most of the kinetic energy to the Switched Reluctance Motor which spins upwards to whatever speed until it matches the connection to the front wheel. At this point the two are running at the same speed and from this point on the standard friction brakes continue to slow the bike further while the Switched Reluctance Motor acts as a flywheel with a freewheel and spins independently.

When it is time to apply the throttle again the energy held in the Switched Reluctance Motor flywheel is translated into electrical energy that is fed backwards to the motor on the rear wheel.

So the process is:

Engage the clutch
Spin up the flywheel

...go through turn

Dump the Switched Reluctance Motor flywheel as electrical energy to the drive motor.

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The critical part would be the gearing... you want to spin the Switched Reluctance Motor flywheel up to speeds like 100,000 rpm if possible.

Design For That Idea

The physical design would be to have a double disk front hub and on the left side have a disc brake and on the right side a large disc that (somehow) would be the point of engagment of the flywheel.

On second thought...

You might even be able to have your disc brake work double duty as the clutch engagement process would involve disc brake pad material that would contact the disc brake itself.

With some refinement of the idea one might even figure out how to make this a direct bolt on for existing bikes. :wink:

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Another tangent might be to replace the disc brake with a clutch and make it so when you apply the brakes there is some engagement that senses "back pressure" as long as the flywheel is still increasing speed (and giving brake force) then you use that but once the speed drops low enough so that the flywheel freewheels then you use the clutch in a way where it directly applies the brake.

This is doable I think.

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The thing not yet mentioned is that Switched Reluctance Motors are not easy to deal with. They are apparently even more complicated as far as circuit design than the RC motor itself... so getting the power back out of the flywheel will involve some sophisticated circuits that would be tough for DIY to be able to deal with..

Be sure to keep us posted with your progress.

gogo said:

Be sure to keep us posted with your progress.

Click to expand...

We are discussing things in the future here. (the word "potential")

The conclusion about RC motor regen for "sport" riders was that it is a complete failure. Since the sport rider accelerates on downhills and brakes really, really hard for turns those are the ONLY places that you have a chance to get any regen in the existing way and such sport behavior makes regen impossible.

So we ponder these things BECAUSE we have admitted that the other way cannot help us.

Just be sure to recognize why we are in this position.

For People With $$$

I'm not going to start this project because I've got other things I'm working on, but if you have the time and $$$ you could start by buying one of these:



http://www.srdrives.com/technology.shtml

...and since they have the software for their product already you could make a giant leap forward in getting it to a point to be able to test the idea.

For a clutch you might just try getting some motorcycle clutch parts and figuring out how to use them as a "clutch / brake / flywheel activator".

Anyway... the idea of the first "KERS for Ebikes" sounds pretty cool to me. 8)

Such systems are presently used on wheelchairs:

http://www.srdrives.com/powered-wheelchair.shtml

safe said:

Just be sure to recognize why we are in this position.

Click to expand...

For the spectre?

The point is that something like KERS could actually be of some value because it prefers to capture things like hard braking. The existing regen system does not work in the environment that a sport rider rides in.

Existing regen makes some sense for someone doing a slow speed cross country trek, but it makes no sense for a hard braking, fast moving sport rider.

KERS, if done well, could actually make sense for sport ebikes.

TPA said:

You mentioned the weight...but the angular momentum would be nightmarish for bicycle handling.

Click to expand...

Oh, yeah, that. Ermmm.... Angular momentum has eluded me in the exact way it comes about and affects operation but it's clearly the governing principle in gyroscopes and tops. I believe the angular momentum would be pointing along the axis of rotation and turning on a plane perpendicular to that axis shouldn't affect that(That is, simply turning left or right). But, when people "turn on a bicycle", then also tilt the bicycle so the change in direction is no longer perfectly perpendicular to the axis of rotation and there'd be some handling issues there. So, I'd imagine the rotating mass would have to be mechanically decoupled from the bicycle, but still attached to direct it left or right... kind of like a ball-joint connection to a kiddy trailer, maybe?

TPA said:

You mentioned the weight...but the angular momentum would be nightmarish for bicycle handling.

Click to expand...

Not only that, but at 20,000 rpm, you'd better have something much stronger than lead to prevent it from flying apart. For 1m radius, I don't think steel would even survive. I gave an example from an old physics textbook here

PaulM said:

Looking further through my old physics textbook, it gives an example of an actual case where a test was done on a steel rotor with a mass of 272 kg and a radius of 38.0 cm. The disk was brought up to speed and at about 14000 rpm, it exploded, destroying much of the test room. The energy of rotation was calculated to be 2.1x10^7 J.

Using my "Engineering Power Tools" converter, this is equivalent to 10.4 lbs of TNT. Or only 5.83 kWh.

Of course, if we guess that this energy was released in 0.5 seconds, that gives a power value of 42 MW.

Click to expand...

I think I'll keep my distance . . .

I've thought of this, but not as a main means of storing energy. The idea was to get something capable of making use of the power from regen when coming to a halt, but lighter then caps. I had imagined something about the size of half a can of pop, maybe an RC outrunner inside with an machined cylinder around it. Seems like it could do it.

You might have missed this... posted elsewhere...

http://www.racecar-engineering.com/articles/technology/281974/f1-kers-bosch-goes-modular.html

“The flywheels are basically a simple electric motor, which run at between 140,000 and 160,000rpm. You spin them up using the drive motor as a generator, and store up the electric energy as rotational energy, the boost is the opposite process and the energy is released as electricity to the motor generator.”

So the secret is to use an actual motor (Switched Reluctance it appears) and use the spinning of the motor AS the flywheel.

It's the best of both worlds...

In essence the motor/flywheel is a "battery". :wink:

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The advantage of a Switched Reluctance motor is that the "core" is made of solid steel and so you are not going to be able to break it apart like some motor that was made up of laminated material.

Bosch seems to think (based on the photo) that Switched Reluctance is the way to go and I had suspected those would get attention because of how strong and simple they are.

Mathurin said:

...maybe an RC outrunner inside with an machined cylinder around it. Seems like it could do it.

Click to expand...

That's how I see it... something about the same size as an RC motor only attached to the front wheel.

The weight needs to be 2-3 lbs at most.

You all are limiting yourselves to regen! As far as stop-and-go regen goes, it actually seems pretty darn smart since it's efficient and doesn't have much of a limit on power like batteries do, which is a concern when stopping quickly. Since most stops are proceeded by a quick start, there's not much time for the flywheel to mechanically dissipate energy which makes it even more appealing.

But as far as a stored energy source... it seems like it could be nifty but there are some serious problems. Maybe energy losses over time could be minimized by using magnetic levitation? Oh, that seems like it'd be fun to figure out how to implement.

Edit: Oh, just read PaulM's post on the material strength. Hmmmm... that's a bummer. Maybe we need to get some futuristic discs, eh? Oh well, it's probably limited to stop and go regen where it seems like it's among the best solutions.

I'm in agreement that a flywheel is the best high energy storage system for storing the braking force. That was the conclusion of the experts who studied KERS.

Pound for pound a flywheel can store more energy than any of the other options such as a battery or an ultracapacitor.

...but I think the genius was to COMBINE the flywheel with the motor.

Bosch used a Switched Reluctance motor. (it appears)

Does everyone get that?

(I've written it several times, but I suspect the beer is taking effect already :lol: )

The genius was that they use an electric motors rotor mass AS the flywheel.

Mathurin said:

[...]

Click to expand...

Disregard, half baked idea, etc.


I've started doing calculations assuming 100kg rider + bike + clothes etc, top speed 32km/h, 36V 40A controller, 10s4p Konion 36V 6Ah pack, fixed drivetrain. But I didn't go very. Thing is, batteries have very much better eff for sucking up regen then the flywheel could. What limits batteries is their charge rate, and given Makita packs charge Konions in 1/2 hr, they can certainly take 2C safely. So the 6Ah battery could suck up to 12a, and any more would go to the flywheel. Now compare that to real-world regen amps:

justin_le said:

This experiment was repeated a total of 5 times in each case with the regen throttle held steady at a different position. The net results are summarized in the graph below, where I have plotted the percentage of the intial kinetic energy that was returned to the battery as a function of the peak regen current for that particular regen throttle position.


You can see that there is a pretty wide range from about 6 amps to 12 amps of regen current where half of the original kinetic energy was recovered. I was rather surprised that the result was this high and over such a broad range, and 6-12 amps is a good figure since it is within the scope of what most modern rechargeable battery chemistries can take for maximum charge current (~0.5-1C, with ebike packs averaging about 10 Ah).

Justin

Click to expand...

And it becomes obvious that the flywheel would essentially be dead weight on this bike, the batteries could already suck up the amps.

Plus the gyroscopic issues can be challenging.

I know that from riding motorcycles is that when your sailing along the gyroscopic effects of the wheels is plenty strong enough to keep the bike upright pretty much irregardless of what your doing. The faster you go, the bigger the forces. Depending on the bike and how much leverage you have it literally becomes impossible to steer the bike. Literally you could come half off the bike and hang on it and it won't fall over. In order to steer the bike you actually have to push the the steering wheel in the opposite direction you want to go so that the bike 'falls' into the turn. It can require significant amounts of force to make the bike fall like that. It is the only way you can steer the bike when your flying along.

(Even at 15-30 mph countersteer method is still the best way to initiate a turn quickly while retaining control. (works for bicycles, too))

If you look at motorcycle racing you'll see plenty of examples of high-speed crashes were the rider hits something hard, is thrown off, the bike wobbles for a bit, and then the riderless bike just takes off straight into a wall.

My fear is that if your using this for regen and you engage in some emergency braking situations that you will literally lose your ability to quickly turn the bike... meaning that you will have the tendency to simply plow straight into the thing your trying to avoid. If your expecting it and your used to it you may be able to modify your riding habits to counter act this effect, but it's still questionable.

I don't know enough of this sort of engineering math to figure out how much force a spinning weight will exert on a bike, but I suspect it will be very significant.

Perhaps you have seen this:
[youtube]7ZmxXJ3qncw[/youtube]

http://www.reverserotatingrotors.com/prototype.html

Ah, so if you have two flywheels running in the opposite directions then they cancel each other out. Good to know.

Just wind up a spring mechanism instead of storing it in a flywheel. It would be much more applicable to stop and go riding in the city than for long downhills, but pretty easy if you can find the right springs. Think of a windup toy, but bigger. I've seen the idea before, so maybe the product already exists.

Here's one some students came up with and tested to about 25% efficiency using a bungee cord to store the energy. I guess it never dawned on them to use some more pulleys to shorten the design, but the contraption works, probably better than most regen. http://www.public.asu.edu/~mgomes1/Bungee_Bike/Web Page FINAL Group3_files/Page1120.htm.

John