# Energy Density of a Capacitor

• posted

How does a capacitor compare with, say, a lead acid battery, energy/weight?

Bret Cahill

• posted

Car batteries have an energy density of about 108 kJ/kg.

A 10,000uF capacitor at 35V weighing about a half kilogram comes in at about 12J/kg.

• posted

Graham

• posted

energy/weight?

Since it takes about 70 watt hours to get a one ton car up to 45 - 50 mph, the _increase_ in conventional battery weight to allow for regenerative braking is 1 kg.

A conventional capacitor would add three (3) orders of magnitude more weight, 1000 kg, ONE METRIC TON, to the regenerative system.

It's impossible to double the weight of the vehicle and come out ahead when the best regenerative systems all operate at less than 50% efficiency.

And that's ignoring the reduced gas mileage cruising.

And that's ignoring the safety issues.

At least 10,000 psi H2 tanks don't leave a crater in the road when they rupture.

Bret Cahill

• posted

energy/weight?

1/2 mv2 = 242kJ = 67 Wh - OK. ( used 22m/s)

To 'allow' for it ? I don't understand your thinking. It's not a capacity issue, it's rate of charge issue. The battery has plenty of capacity but doesn't much like fast discharge or charge rates and these compromise battery life.

No-one's using conventional capacitors !

You're barking up the wrong tree.

Let's say your cas has a 400V power bus. To accelerate from zero to 50 mph take that 70Wh. Let's say the car does it in 15 secs at a constant acceleration. That's 252 kJ in 15 secs =

16.8 kW = 42 A.

Decelartion has to be faster. Maybe 3 secs ? If we do the same sums then with regenerative braking the battery would have to accept charge at a rate of 210A ( 5x the above ). All the above obvioulsy assuming 100% efficiency for ease of calculation.

In comparison the car probably cruises using no more than 10kW. Which is 25A.

So the battery's designed to last a long time with say a 25A discharge and the super-cap 'takes the strain' of acceleration and braking. It's really quite simple.

The Mini I mentioned in another post for example uses an 11F 350V supercap.

That's 673 kJ. Using the above equations that's good for one burst of acceleration to about 85 mph before taking the battery's contribution into account.

It's 21kWh battery contains 74 MJ. There's no comparison. The battery is the long term power source.

Graham

• posted

Two pounds additional conventional battery weight will get a one ton motor vehicle up to 45 - 50 mph while it takes a ton of conventional cap to store the same amount of energy.

Since the best regenerative systems all operate at less than 50% efficiency, it's impossible to EVER recoup the energy wasted in a system that DOUBLES the weight of the vehicle REGARDLESS of the driving situation.

And we haven't even gotten to the lower mpg cruising.with a one ton cap on board.

And we haven't even gotten to the safety issue of releasing 70 watt hours of energy in microseconds [hundreds of megawatts] in case of a short.

At least 10,000 psi H2 tanks don't leave a crater in the road when they rupture.

Bret Cahill

• posted

Just repeating yourself now ? How's that echo in the vacuum of your head going ?

Graham

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Call up Homeland Security and tell them you want to put 70 watt hour super capacitors in motor vehicles.

Just don't mention my name.

Bret Cahill

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Why ?

Graham

• posted

unless defective the battery is more that 5 times better, probably much more.

Bye. Jasen

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They don't, except in history books. They energy in capacitors arises from that they charge/discharge in microseconds. The energy in lead acid batteries comes from sponge lead, which is where it's weight comes from.

• posted

Yup. More like 10,000.

John

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Honda has an 8 farad capacitor charged to 430 volts that can power an EV for a mile or more. I don't know how big the thing is, but a 50aH,

12 volt lead acid battery would be 600 watts for one hour (600wH) and the 8 farad capacitor at 430 volts is 206 watts for one hour (206wH). Now, unless I screwed up my math somewhere, it looks like the capacitor has about 1/3 the capacity of a 50aH lead acid battery. But, the capacitor is probably several times bigger than the average automobile battery, so the energy density may only be only 1/10 or 1/20 that of the battery. What do you think?

-Bill

• posted

Probably right. But the reason they're using capacitors is because they're using hydrogen fuel cells, So you want an electric system that produce arcs, light batteries systems do.

• posted

Current state of the art super capacitors have an energy density of about 3.1 Wh/kg about 15% of what current lead acid batteries have. Their costs are over one order of magnitude greater than current Li-ion cells. Capacitors for engineered systems are only used for high peak power and high charge/discharge efficiency. Good applications are accelerating a garbage truck from zero to ten mph, and back to zero in the 100 feet between houses. Very little energy, but lots of power. For energy storage to give long range they are a nonstarter.

```--
Mike

Some say we must tax corporations more.  What they do not understand is that```
• posted

That's on a cost/energy basis?

Regenerative braking EV makes sense on route fleet delivery vehicles because the range is known or can be managed. There are no surprises. All trucks wind up at the same garage at night. A mechanic is often available. It's politically possible to force USPS to adopt new technology.

Since garbage trucks are expensive anyway they ought to do them first. Besides, what's most obnoxious about a garbage truck isn't the smell, but the engine noise.

To have any range, EVs wind up having enough batteries for all the power they need.

A 70 watt-hr charge/discharge doesn't impact battery life all that much so a capacitor isn't much of an advantage.

Just do it with the individual income tax.

Bret Cahill

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I think you confuse energy and power. The batteries have the energy, the capacitors provide the power. You need both.

Yes it is, because the little 70 watt-hr capacitor can deliver all it's energy in a few seconds. 70 watts for an hour is the same as 252,000 watts for 1 second.At 746 watts per horsepower, that's 252,000 / 746 =

338 horse power. The battery probably can't do that because the internal resistance is too high.

-Bill

• posted

About one mile's worth of energy / hp.

The Tesla can cruise 250 miles.

Tesla batteries can put out 250 hp.

The Tesla is a tiny car so the problem with batteries isn't that their power density is too low but that they are too much like capacitors:

The energy density of batteries is too low.

You get all the power you need with any battery only EV with any range over 100 miles.

That might be useful in a short range fleet delivery vehicle. USPS mail carriers rarely go over 15 - 20 miles/day. In that case a few cheap deep cycle lead acid batteries and a capacitor might make sense.

For longer trips they can add a portable gen set to convert it to a hybrid.

Bret Cahill

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That is because you are 'Bret', the spoiled brat that has no concept of quads....

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I'm a populist, that is, I'm aware of the political aspects of prying 'em out of their SUVs.

Bret Cahill

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