A recent adoption of electric vehicles by the US automotive industry indicates that electrification could become viable in general aviation. This is an exciting development for an industry that has not kept pace with its automotive, or commercial aviation counterparts.

## What about Fully Electric?

Battery energy density (measured in watt hours per kilogram) is too low in commercially available batteries. In spite of that, trainer aircraft or extremely efficient airframes flying at best glide with solar panels on the wings or other tricks up their sleeves have already been demonstrated to be successful.

## Hybrid Electric Justification

Electric motors are light and compact for their power outputs compared to their dinosaur burning counterparts. For the same weight, you can put a higher power electric motor in place of an internal combustion engine. The caveat is that you cannot run it for long or you will need a lot of batteries. An example of the power/weight discrepancy:

Motor | Horsepower | Weight (lbs) | HP per Pound |

Titan X340 (combustion engine) | 180 | 290 | 0.62 |

Ford M-9000-MACHE (electric) | 280 | 205 | 1.36 |

*Comparing Electric and Gas Motors*

For every pound you add to the airplane, you’re getting more than double the horsepower using the MACH-E motor. (It also costs $4,000, the X340 is north of $25,000).

How do we take advantage of the remarkable power to weight of electric motors, and minimize the effect of terrible energy density of batteries when compared to gasoline?

Some would say you wait for better battery energy densities. Some would say an onboard gas-powered generator. Others (myself included) would remember the Cessna Skymaster.

The Skymaster has a unique configuration of in-line motors, one for pushing, and one for pulling. Here are some specifications:

Unlike other twin engine aircraft, the Skymaster can run on one motor without yawing or rolling toward the dead motor. This makes the Skymaster an interesting candidate for hybrid electrification.

## Hybrid Goals

Before embarking on the herculean process of making a real hybrid aircraft, it is worth taking the time to understand what it should do. I’ll set the following goals:

- Minimum 850lb useful load
- Cruise speed above 90mph
- Improved takeoff performance
- Minimum range 350 miles
- Minimum endurance 3 hours

I feel these goals represent a minimum acceptable range, endurance, and speed to the average recreational pilot. To achieve the above, we need to size the motors, fuel capacity, battery capacity, and estimate aircraft performance.

## Current Skymaster Performance

A bone stock Skymaster 337D meets the goals. Using the performance numbers above, the Skymaster can go 965 miles on 80 gallons of gas at 144 mph. From that, I can work out how much energy is consumed. A gallon of 100LL contains 46.8 MJ (megajoules) per Kg and weighs 6 lbs per gallon.

$$80\ gal*6\frac{lb}{gal}*.4535\frac{kg}{lb}*46.8\frac{MJ}{Kg}=10,187\ MJ$$

That is a lot of energy, but combustion engines are pretty inefficient. How inefficient? Here I must make a big assumption. I will assume the Skymaster’s motors convert energy into power at 30% efficiency. This means that for every unit of energy entering the motor, only 30% of that energy makes power at the propshaft.

$$10,187*.3=3,056\ MJ\ = 849\ kWh$$

Now we know how much energy it takes to get the Skymaster to go 965 miles at 144mph. How much power \(P\) is that if it is constant over the duration of the flight?

$$P = 144\frac{miles}{hour}*\frac{1}{965\ miles}*849\ kWh=126.7\ kW=170\ HP$$

If the Wikipedia numbers are good, the Skymaster motors put out a combined 170 horsepower to maintain economy cruise. This seems about right, given the motors are rated for 210 horsepower each, this equates to 40% power.

We can further check this figure by using the power required equation to see if we get a “sane” drag coefficient for the Skymaster:

$$P_R=\frac{\rho}{2\eta}v^3C_D S = \frac{1.225}{2(.75)}64.37^3*C_D*18.7=126,700$$

$$C_D=.03$$

Wikipedia claims the drag coefficient of a Cessna 172 is .027, so the Skymaster’s \(C_D\) seems reasonable. However, I don’t know what area the Cessna 172 data used.

*Note I used sea level air density instead of 10,000ft air density

## Matching Current Performance

The hybrid Skymaster will rely on the gas motor to make the vast majority of cruise power to meet range and endurance goals. This is a result of the low energy densities available in batteries. As an example, if the gas and electric motors work equally to generate the 170HP found above, the electric motor must make 85HP or 63.4kW. In one hour that motor will burn through (you guessed it) 63.4kWh of energy. 63.4kWh of energy in battery packs at 205 Wh per kg will weigh 681 pounds. I’m not going to suggest putting a 681 pound battery pack into the Skymaster for a 1 hour economy cruise.

To match the economy cruise performance of the current Skymaster, the hybrid Skymaster will need to output the same power, 170HP. Assuming it is impractical to run a gas motor over 70% of its rated power constantly, we can get 147HP from the gas motor, leaving the electric motor to take up the slack of 23HP. If the electric motor only needs to produce 23HP in cruise, for that same 681 pound battery pack, I calculate an economy cruise duration of 3.7 hours. Not bad – Still that battery pack is too heavy. To maintain a useful load of 850 lbs the battery pack cannot weigh more than the gross minus empty minus full gas minus 850 which I work out to 535 lbs.*

*This makes a new assumption that the electric powerplant, controller, inverter, wiring, etc. is equal to the weight of the gas motor installation it is replacing.

$$4400\ gross -2655\ empty-360\ gas-850\ remaining=535\ lb$$

A 535 lb battery pack burning down at 23HP gives a 2.9 hour economy cruise duration. This meets the following goals:

- Minimum 850lb useful load
- Cruise speed above 90mph
- Minimum range 350 miles
- Minimum endurance 3 hours

So how does one get that extra hour of endurance? Go slower. How slow? Lets find out.

## Moving the Goalposts

Unable to match the current Skymaster performance in a hybrid configuration, I can still play to the strengths of electric motors. It should be possible to capture improved takeoff performance while maintaining a tolerable range, endurance, and speed by slowing down. There should be a range of speeds above 90mph that meet the 350 mile range, 3 hour endurance goals. To find that range, I would ideally have some more performance figures for the stock Skymaster so that I could interpolate between them, but I don’t.

Using what I know from Wikipedia I can try to find best range and best endurance speeds. Best range is the speed that maximizes distance over the surface of the earth for all of the energy available (gas and batteries). Best endurance is the speed that maximizes time aloft for all of the energy available.

The lift generated must equal the weight of the aircraft. Assuming operating at max gross weight and economy cruise:

$$L=\frac{1}{2}\rho v^2 C_L A$$

In SI units:

$$1996=\frac{1}{2}(1.225)(64.37^2)C_L(18.7)$$

$$C_L=.0421$$

At economy cruise I get a ratio of \(\frac{C_L}{C_D}=1.405\) This is a horrendous lift to drag ratio. I have a hard time believing the cruise glide ratio is 1.405:1. A brick probably has a better glide ratio than 1.405:1. The lift equation baked in no assumptions, but neither the \(C_D\) or \(C_L\) figures allow me to extrapolate to different speeds. So its time to get creative.

I know the aircraft needs to slow down in order to improve range and endurance, but it cannot slow down too much or lift induced drag will reduce efficiency of the aircraft:

I could buy a POH for the Cessna 337 and find the published best glide speed, but instead I’ll make an educated guess and assume that the bird can be slowed down to 130mph without getting on the backside of the power curve. This means the new lift coefficient is:

$$1996=\frac{1}{2}(1.225)(58.1152^2)C_L(18.7)$$

$$C_L=.0515$$

This means that we will require a 22% increase in lift coefficient, at the cost of lift induced drag. Unfortunately it is difficult to solve for how much lift-induced drag the aircraft will take on to fly at this slower speed. Given this speed is likely to be above best glide, it is reasonable to assume that the aircraft will lose more parasitic drag than it gains in induced drag. I’ll conservatively assume the drag coefficient must increase proportionally by 22% in order to accommodate the increase in required lift coefficient. Now power required to maintain level flight is:

$$P_R=\frac{\rho}{2\eta}v^3C_D S = \frac{1.225}{2(.75)} 58.1152^3*.03*1.22*18.7=109,708$$

This is almost 23 fewer horsepower than is required to maintain 144mph. Now that the aircraft only needs 147HP to stay aloft, the gas motor can be dialed back and the electric motor can be set to a power level that is most advantageous for the mission.

## Fly Slower and Look Good Doing It

I’ll refresh where we’re at. With some assumptions made, it should take 109.708 kW (147HP) to fly level at 130mph. At our disposal is a 210hp gas motor and a 280hp electric motor. The aircraft needs to meet the following goals:

- Minimum 850lb useful load
- Cruise speed above 90mph
- Minimum range 350 miles
- Minimum endurance 3 hours

The things that need to be determined:

- Battery Quantity
- Cruise power settings for electric and gas motors

### A Quick Aside

Battery weight was solved for above and I decided this aircraft should tolerate 535lbs of the stuff. At an energy density of 200 Wh per Kg – this is 48,534 watt hours of energy. Now there is a big constraint I haven’t mentioned which is discharge rate. If the electric motor is run at max throttle, it will be pulling 209kW of power from the batteries. Ignoring limitations with battery chemistry, the electric motor could only be run at max throttle for about 14 minutes.

Here is a plot showing how long you can run the motor in minutes (y axis) over throttle % (x axis):

To further complicate this problem, high charge and discharge rates of batteries is problematic from the perspective of battery longevity, temperature, cell damage, and probably more. I’ll make another big assumption here, that the electric motor should not be operated at a power that exceeds a c-rate of 4, which means the motor should not be operated above a power that would discharge the entire battery in 15 minutes (260 HP).

Modern batteries can probably be operated at high c-rates for short periods of time (less than a minute) but should be operated at a c-rate of less than 1 (65 HP in this case) for long durations. This is not a field I am well versed in, so do your own research. This is the end of the quick aside…

## Fly Slower and Look Good Doing It Part 2

A stock Skymaster takes about 17 seconds to get itself airborne according to a Youtube video at a field elevation of 1700 ft. From that, it is reasonable to assume that full power from the electric motor is not going to be required for more than a minute or two. Reducing the power level shortly after takeoff isn’t an action pilots find themselves drawn to – so from a practical sense, it may make sense to have a smaller motor, more batteries, a throttle limiter, or another alternative.

I’ll assume the cowboy pilot of this hybrid-electric Skymaster is heroic enough to bring the throttle back in such a way that they do not use more than 20% of the battery capacity to take-off and reach a cruise altitude. Is that reasonable? Conservatively the Skymaster at full bore can climb at 1,000 fpm. This hybrid bird (hybird?) has an extra 50HP over the stock configuration. In 3 minutes you should expect to be cresting 3,000ft above field elevation on a standard day. So yes, its reasonable.

Now there are only 38,827 wh remaining in the battery. To achieve a 3 hour endurance (with 30 minute reserve) the pilot can only run the electric motor at a paltry 15 HP. Is this enough? Why yes it is.

147HP is required to maintain the 130mph cruise, and \(147-15=132\ HP\). This means that the gas motor will need to be run at 63% of rated power to pick up the slack of the electric motor.

## Lets Wrap This Up…

I had previously set some goals:

- Minimum 850lb useful load
- Cruise speed above 90mph
- Minimum range 350 miles
- Minimum endurance 3 hours
- More takeoff power

These goals have been exceeded. This theoretical configuration of the Skymaster gets us to:

- 850lb useful load
- Cruise speed of 130mph
- Range of 390 miles (ignoring extra cruising on the gas motor only)
- Minimum endurance 3 hours (with 30 minute reserve)
- 50 extra horsepower for takeoff

## One More Thing

One could also dial the electric motor back to less than 15HP and go even further, at this point, the optimization of the aircraft configuration becomes flight specific and I am not particularly interested in taking this there.

If one were to undertake a project like this, estimating weight savings by removing extraneous equipment might present a valuable exercise. Further, adding solar panels to the top skin of the wings, fuselage, and horizontal stabilizer could net around 3kW in perfect conditions, which isn’t quite so useful in flight, but it is extremely useful on the ground.

If someone out there would like to have a hybrid-electric Skymaster, and wants me to get involved in their project, have your people call my people.