Horsepower required for aerodynmic drag at 55MPH

[TonyWilliams]

To compare, drag area is the frontal area times drag coefficient. The Prius has a drag area of 6.2 sq ft. The Spark EV has a drag area of 8.8 sq ft. That's almost 30% more.

Referring to my previous equations, one thing to remember is that density over temperature doesn't play much of a role at a specific altitude. For three reasons...1) the variation in density with temperature is about 0.002 kg/m^2 per degree F for a set altitude..say at sea level or 500ft or whatever one would expect a car to be at in everyday normal driving.

Well, folks "normally" drive at all elevations and all temperatures. Just because your "normal" is at sea level with southern California non-weather does NOT mean that both temperature AND elevation are not important to the equation of air density.

Here's some examples of "air density equivalent elevation" in feet above seal level and the relative density to "standard" (standard is sea level, 59F, air pressure 29.92 inches), which will mean a whole lot more to folks than "0.002 kg/m^2 per degree F". I have omitted the variations in standard pressure, since those are indeed smaller adjustments (that you make no mention of). Humidity is also omitted, even though it also has a small impact on air density:


Temperature ------ Sea level -------- 5000 feet --------- 10000 feet
-------------------Santa Barbara------- Denver -------- mountain pass

-40F -------minus 8000 ft (123%) - minus 900 ft (102%)--- +5500 ft (85%)

59F ---------- sea level (100%) ----- +6200 ft (83%) ------ +12200 ft (69%)

120F ----------- +3800 (90%) ------ +9800 ft (74%) ------ eh, not really possible!


The point of this exercise is to show that temperature is a LARGE determiner of air density. Through the temperature extremes that one might find on inhabited portions of planet earth, air density can change more than 30% at the same elevation.

You'll also be advised that your metric air pressure density is kg/m^3, not ^2, as you write:

Temp -------sea level ----------- 5000 feet ---------- 10000 feet

-40F ----- 1.513kg/m^3 ------ 1.259kg/m^3 ------ 1.04kg/m^3

59F ------ 1.224kg/m^3 ------ 1.019kg/m^3 ------ 0.842kg/m^3

120F ----- 1.095kg/m^3 ----- 0.911kg/m^3 ------- 0.753kg/m^3


Air density at the same elevation is 1/3 less at the same temperature, from sea level to 10,000 feet elevation.

It is also 1/3 less at the same altitude, between -40F and +120F.

2) it's a linear relation within the equation unlike velocity that increases on a squared relationship.

So, because the variable is linear, you omit it? There are other linear data points, too.

 

[nozferatu]

The slope of the air density to temperature ratios within the normal temperature ranges most people see and altitude variations within which most of us drive is exactly as I mentioned it.

Using rudimentary algebra, you can easily calculate the density based at a different temperature based on a known density measurement. 0.002 kg/m^3 per degree F is a small variation. It's very easy to calculate and I can show you how it's done if you wish.

Our cars are not aircraft where we are going to see big variations due to huge altitude changes. So it is moot to show how much density changes in operating regimes we are not going to find ourselves...ever. Humidity and "standard pressure" are not needed to be mentioned here even though I am fully aware of them. There is no need because they have little to no impact in the operating regimes we are talking about.

So please state what the density variation is over a 50 degree temperature at a set altitude...say at 1000ft? And tell us how much of an impact it makes on Force required. I already know.

I never said I omitted density from the calculation or said it doesn't make an impact. You may have missed my last paragraph it seems as it's all explained there very clearly.

I'll reiterate it here:

Referring to my previous equations, one thing to remember is that density over temperature doesn't play much of a role at a specific altitude. For three reasons...1) the variation in density with temperature is about 0.002 kg/m^3 per degree F for a set altitude..say at sea level or 500ft or whatever one would expect a car to be at in everyday normal driving. 2) it's a linear relation within the equation unlike velocity that increases on a squared relationship. 3) The density only plays a role in only one portion of the Force equation. So over a 50 degree F spread, the density will change only one portion of the equation by about 10%. The same effect applies for mass variations.

I know what the units are but thanks for catching my typo.

 

[SparkevBlogspot]

It's easy enough to see the actual power with SparkEV. I saw 11 kW when driving constant 55 mph over several miles of flat road with slight ups and downs for small grades. 11 kW is about 15 HP.

http://sparkev.blogspot.com/2015/05/freeway-efficiency.html

While not in my blog, I never got over about 30 kW even on grades between LA and San Diego, 40 HP would be enough for most driving at 55 mph, but what is the maximum grade you need to climb?

 

[NORTON]

...don't worry about the front license plate or the boxy-back!

Right! The miles/kWh numbers above are what really matters !

 

[fox]

So has anyone done anything to improve the aero of the spark EV as I'd like to get started
1. covering up rear wheel wells
2. possibly the same to the front if I can figure out a working design
3. lighter wheels and tires.

 

[NORTON]

So has anyone done anything to improve the aero of the spark EV as I'd like to get started
1. covering up rear wheel wells
2. possibly the same to the front if I can figure out a working design
3. lighter wheels and tires.

The EV Spark is already more aero then the gasser. (claimed).

Some other ideas:

1. Lexan 'aero wheel disc'. You know, totally sealing the wheel. Clear for testing will do. 4 Ty-raps can hold them in place. (the brakes rarely need any cooling as they rarely get used !)
2. The rear wheel skirts can be made of this material also. Attached with that 'industrial' velcro, (nothing permanent, easy removal).
3. That brush material you see on the wheel opening of some buses and large trucks would be an easy aero seal for the front wheels. It looks like thin, tall push broom material on a metal strip.
4. A series of different sized rows of vortex generators all along the the sides and the top of back of the car.
5. Better yet! One of those aero tails you see on some semi truck. (clear lexan)
6. Rubber air dams front and sides. Let them almost drag! (not sure about this one.. the bottom of the car is already smooth. You don't see this on some record setting efficiency cars...)
7. < 185 tires all around. My Geo Metro ran 145's !

With all the electron cost savings from these aero mods you could buy yourself an extra beer on Friday!!

 

[Planerench]

Could you hook up a tow rope with a strain gauge and directly measure load at speed?