# Are LiPo really 100 times more energy dense than model rockets?

Lately I've been interested in comparing the energy density of model rocket engines to lithium polymer batteries (attached to motors and propellers) for propelling things upwards.

To get a feel for this, I decided to compare an Estes C6-5 motor to a 3DR Iris + quadcopter.

Estes C6-5 has initial mass of 25.8g, and produces 10 N s total impulse. So, the "Impulse density" is about 10 N s / 25.8g = 0.38 N s g^-1.

3DR Iris+ weighs 1282g without battery. 3.5ah battery weighs 250g and will power hover for about 20 minutes (so about 10.5a draw). Thrust produced to hover on Earth is 9.8N kg^-1 * 1.532 kg = 14.7N. "Impulse density" is 14.7N * 1200s / 250g = 70.6 N s g^-1 .

So, according to my math here, the LiPo is about 0.38/70.6 = 186 times more energy dense than the model rocket engine.

Of course, the model rocket engine will lose 12.48g of propellant by the end of the flight so it will be effectively a little lighter, but that's not going to affect things by a factor of 100.

Does this seem right to you? Am I missing anything?

• How are you measuring the impulse of the model rocket engine?
– Chuck
Commented May 29, 2015 at 12:52
• Didn't measure it -- read it off the datasheet. The link in the question also takes you to the product page where you can see the datasheet. Incidentally, a friend of mine has actually measured them for a class project though, and found them to match the datasheets very closely. Commented May 29, 2015 at 16:25
• Upon first reading, your calculations seem right to me. It surprised me that the energy density of the Li Poly batteries was so much more than the rocket engine. What I've been noodling on is how to convert that energy into thrust to create an all electric model rocket. I got as far as realizing that dumping electricity from a battery into a capacitor might result in fast enough power discharge, but I am stuck on converting that electricity into thrust for a model rocket. Any ideas? Commented Oct 17, 2017 at 20:54
• Welcome to Robotics Jonathan Koomey. On Stack exchange answers need to answer the question. If you have a related question, it should be asked as a new question (ideally referencing this one). Note that we prefer practical, answerable questions based on actual problems that you face. Please take a look at How to Ask and tour for more information on how stack exchange works. For advice on how to write a good question, see the Robotics question checklist. Commented Oct 18, 2017 at 17:19
• There's a very big difference in lift efficiency of propeller blades versus rockets. I believe chemical fuels like gasoline are actually about 10 times as energy-dense as batteries. Commented Oct 20, 2017 at 19:46

The short answer is "Yes", Rocket motors are less energy dense because they are built to expend that energy more quickly, while Lithium Ion Polymer batteries are designed to work longer. However saying that they are "100 times" cannot always be correct.

The reasoning being that not all Lithium Ion Polymer batteries are made equal. You have different C rates, cell density (affects C AND mAh), and different mAh. For example the Zippy 3S 20C/40C 3000 mAh battery weighs about the same as the Mutistar 3S 10C/20C 5200mAh. In general it would be correct to say that LiPo batteries store more energy than model rocket engines, this because of the different run times of the two fuel sources. A capacitor may discharge more voltage and amperage than a battery, but the battery can generally run longer.

• Fair point that rockets would effectively have a very high equivalent C rating. To improve your answer, you can calculate this. Energy density (assuming that's what you mean by "cell density") is capacity / mass and a higher discharge (C) rating tends to mean lower energy density. It seems your argument should start with "The short answer is 'yes'". Rocket motors are less energy dense because they are built to expend that energy more quickly. Commented May 29, 2015 at 6:37
• Energy density and cell density are different cell density is how tightly packed the cation, anion, and the insulators are packed. This affects a lot of other factors. Commented May 29, 2015 at 13:06
• Can you provide a reference for this idea of "cell density"? It's not standard lipo terminology as far as I know. Commented May 29, 2015 at 16:27

I think the main difference is that the energy in the rocket engine is (probably, I'm not a rocket scientist) far less effectively used than the one of the LiPo. Also, the actual weight of the fuel in the rocket engines might be way lower than the weight of the engine (so your masses are not consistent, one is only the battery/"fuel", one includes the motor).

It would be interesting comparing the weight of a LiPo/Motor/Quadcopter with a Rocket engine with similar thrust, to see how size effects play into this.

For a "similar" comparison of a zippo vs a phone battery, look here.

• The two in my question do have similar thrust -- one provides 10N and the other 14.7N. Also, I did discuss the loss of propellant mass in my question -- 12.8g of the 25.8g motor is propellant. Interesting about the zippo. However, this doesn't answer my question. Commented May 12, 2015 at 13:41
• Oh, sry, I somehow missed that. If only 12.8g is propellant then that's what you want to divide the impulse through, I think. I guess a lot of the energy of the rocket motor goes into heating the air and other losses, whereas the Quadcopter could be more efficient. Commented May 12, 2015 at 16:41