Prius c has worse mpg than Gen III on Fuelly

There's more at work here than the Cd. The Gen III went to a larger engine to help improve its Hwy mileage over the Gen II. The c continues with a 1.5 L engine so it's probably working harder on the highway.

 

This is why I said the Prius 'c', but with a lower Cd. Everything the same except for one parameter.

The larger ICE in the G3 is partly to offset the higher weight, and partly to give the car more hill and passing ability, and put less demand on the traction battery. It will not give a fuel advantage at steady state on level roads at moderate highway speeds. I say this mostly out of experience that until RPM > ~ 2500 the ICE friction does not play much of a role in fuel economy.

BTW, has my kitten been hanging out at your place ?

 

The problem with aero drag is, as speed goes up linear, drag goes up exponentially.

The problem for the C is the shape of the rear end (which literally drags air at high speeds). If you really want a high mpg hiway car, get rid of the outside rear view mirrors, put moon caps on the front wheels, rear wheel skirts on the back fenders, a smooth pan underneath and a boat tail on the back of the C and you will likely net 70+mpg at 70 mph.

 

This table is by Wayne Brown using a G2 Prius:



You will have to play some arithmetic games to figure out the 'C'.
E.g.,
Air friction
@40 mph: 152.8 - 107.26 = 45.54 Wh/mile
@ 70 mph: 250.3 - 110.6 = 139.7 Wh/mile
Difference: 139.7 - 45.54 = 94.16 Wh/mile

If the Cd increases from 0.25 to 0.28,
@40 mph: (45.54)(28/25) = 51 Wh/mile
@70 mph: (139.7)(25/25) = 156.46

Combine numbers, and we get total friction @70 mph in a G2 Prius with a 0.28 Cd = 110.6+156.46 = 267.06
The total Wh/mile in a less aero G2 Prius increases by 267.06/250.3 = 6.7%.

Call it 3 - 3.5 mpg. As an aside, this is why AG quite correctly points out that a large fraction (perhaps the majority) of the difference between a Prius and a mediocre Ford hybrid are the aero differences.

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Above is the laborious and pedantic approach. I'm usually much lazier, and just mentally calculate the following: 28 is about 12% more than 25 (the increase in Cd.)
Since air friction accounts for some 50 - 60% of total friction at usual highway speeds, the increased Cd adds 6 - 7% more energy consumption.

 

Shouldn't that be quadratically or polynomially?

An exponential increase would have it glowing as a meteoric fireball before it reaches the speeds of the commercial airliners I see flying overhead.

 

Does it ? I thought linear meant the exponent = 0.

As in: Linear friction is proportional to V^0, while
Air friction is proportional to V^2

I have taken 'quadratic' to mean a polynomial whose highest degree is two.

I admit, HS math was a long time ago.

 

I think he was referring to the drag coefficient being exponentially increased. It wouldn't take much speed to make you a flaming comet if that were the case.

 

Yes, I was simply referring to speed going up linear like 65, 66, 67, 68 etc and aero drag going up as in the chart Sagebrush posted.

 

Don't remember where I read it, maybe cleanmpg.com. They designed the Priuc C mpg meter to be more acturate whereas the Prius and Prius V are know to be slightly over optimistic, especially if you floor it.

 

If you want to get "mathematically correct" ok, I call uncle. All I know is that a 20 mile increase in speed can make a huge difference in aero drag. I do believe the correct term is exponentially because the amount it goes up gets more and more with every linear increase in speed as evidenced by the chart above. If we go to 150 and beyond, the numbers get crazy big and increase dramatically for every 5 mph. If you go to 300 mph, the amount of power required is insane.

 

X^2 is in the polynomial family, specifically quadratic. In polynomials, the exponents are always fixed.

2^X is exponential. In exponentials, the variable is part of the exponent. Once X gets much above unity, growth becomes explosive compared to even polynomials.

 

And a different engine, two different Motor Generators, a much smaller HV Battery in the c, a different transaxle, and a different body.
In fact, name parts that are the same, I am curious.

I do not recall mentioning any differences in speed or handling, But

C/D Prius c
Top speed (drag limited): 102 mph
Roadholding, 300-ft-dia skidpad: 0.79 g
2012 Toyota Prius C Instrumented Test – Review – Car and Driver

C/D Prius Liftback
Top speed (drag limited): 115
Roadholding, 300-ft-dia skidpad: .81 g
Toyota Prius Reviews - Toyota Prius Price, Photos, and Specs - CARandDRIVER

 

I put the figures from the Wayne Brown chart into a spreadsheet, extracted the aerodynamic drag portion, and did a curve fit. R-squared is unity when fitting to a polynomial of N=2, or quadratic. When fitting to an exponential curve, r-squared is no longer unity. So his figures are polynomial, not exponential.

Computing from his chart, aerodynamic drag alone (mechanical drag excluded) is 2.4 horsepower at 40 mph, and 19.5 hp at 80 mph.

Extrapolating out to 150 mph, the quadratic curve fit reads 129 hp. The exponential fit reads 430 hp.

Continuing to Mach 1, set to 760 mph for this exercise, I get about 17,000 hp for quadratic, and between 2 and 3 trillion hp for exponential. The former is hot, but the later is a meteoric fireball. The former seems realistic for jet fighters, the later does not.

 

hmm, so one would expect an 8x difference. 2.4 * 8 = 19.2. Pretty close

I find it easier to just leave the units in Wh/mile:
At 40 mph, 45.5344 Wh/mile aero energy reqs
At 80 mph, 182.4652 Wh/mile aero energy reqs

182.4652/45.5344 = 4.007194561
Remarkably close to expected 4x

 

But there will come a point on the chat that the drag curve becomes nearly vertical and the 8x difference will not be accurate.

 

1) I'm not a math whiz (at all). It does seem realistic to Mach 1 but, there will eventually become a point (not sure what speed) of near vertical drag curve .

When that happens will the polynomial or quadratic still work?

 

Depends on if you're talking about the average velocity of an unladen swallow that is European or African.

 

I need to go back to school.

 

Me too

 

I'm too old, grouchy, and independent to go back to school.

A quadratic is just one of the simplest members the polynomial family. Did you mean to ask about exponential?

As far as mathematical functions are concerned, 'near vertical' is just a matter of perspective or scale. All the functions mentioned here will get there, but an exponential function gets there much quicker and much steeper. In this case, the exponential curve will be prohibitively steep at a speed where a B52 or large commercial airliner could, in reality, still carry the car under its wing without leaving the fireball trail required by an exponential extrapolation of Wayne's chart.

Real air drag is probably somewhat more complicated than a simple quadratic function at high speeds, especially when crossing through mach 1. But it is clearly not an exponential function.