Horsepower required for aerodynmic drag at 55MPH

I have been trying to get this number for the Spark EV without success. It is critical for predicting efficiency at higher speeds.

Iknow the CD is ~.33. What is the cross sectional area? What is the simple formula for using these numbers to derive HP vs speed? Forget Reynolds numbers, I'm not going supersonic. I have seen numbers published for autos which give the HP needed to overcome drag at 55mph. These are typically around 5 HP. They also give HP required to overcome rolling resistance.

Another question: How much reduction in drag does the active grille provide?

The reason the Spark has a relatively high Cd compared to a Prius(.25) has to do with cooling requirements for battery and motor.

Not sure if this is useful for what you are trying to do, but I found this calculator online. You just need to estimate the frontal area...

http://www.wallaceracing.com/Calculate%20HP%20For%20Speed.php

Can I slip this little query in somehow:
Any thoughts on the increased drag of mounting the front license plate? Having a flat plate out front pushing against the flow, is not aerodynamic is it?

Pawl said:

Can I slip this little query in somehow:
Any thoughts on the increased drag of mounting the front license plate? Having a flat plate out front pushing against the flow, is not aerodynamic is it?

Click to expand...

Maybe bend it so it slopes maybe ?

JackHickey said:

Iknow the CD is ~.33. ....

The reason the Spark has a relatively high Cd compared to a Prius(.25) has to do with cooling requirements for battery and motor.

Click to expand...

Cooling requirements? I doubt that has any effect. The Prius has a finely tuned aerodynamic shape. Compare that to the overly tall box-like shape of the Spark. I am not surprised in the least at the much higher Cd.

I'm not an expert in aerodynamics but driving in Oregon gives a few insights that may not be readily apparent in Calif. When it's raining (when isn't it here?) the back of the Spark gets incredibly dirty very fast. This tells me that there is a significant low pressure area behind the car. That partial vacuum will pull on the car, thus increasing drag. I'll bet you'd get better rewards working on this than by concentrating on the front license plate - and not catch the eye of officer O'Malley.

Any experts out there please feel free to poke holes in this theory.

Here's data at 62mph ground speed, just convert kW to HP.

Nissan
LEAF - 4 miles per kWh (250 wattHours per mile) = 15.5kW

BMW
i3 - 4.7 miles per kWh (213 wattHours per mile) = 13.2kW

VW
eGolf - 4.1 miles per kWh (244 wattHours per mile) = 15.1kW

GM / Chevrolet
2014 Spark EV - 5 miles per kWh (200 wattHours per mile) = 12.4kW

2015 Spark EV - 5 miles per kWh (200 wattHours per mile) = 12.4kW

Mercedes
B-Class ED - 3.6*** miles per kWh (278 wattHours per mile) = 17.2kW
*** Mercedes consumption meter is calibrated so that 3.6 miles per kWh will show 3.0 on the dash. The correction factor is 83.7%, or 1.2

Toyota
Rav4 EV - 3.4 miles per kWh (295 wattHours per mile) = 18.3kW

The forces acting on the car are caused by internal, tire, and air resistance. The resultant of these forces, the total drag force, Fd, can be estimated by the following equation:

Fd = cR * m * g + (1/2) * p *cD * A * V(squared).

Where:

cR = coefficient of rolling resistance
cD = drag coefficient
m = mass of vehicle [kg]
Af = frontal surface area [m2]
g = 9.8 m/s
p = density of air, 1.2 kg/m3 @ sea level
V = velocity (m/sec)

So,

m (SparkEV) = 2900 lbs = 1315 kg
cD = .33
cR = .01-0.015 (ordinary tires on regular smooth concrete)
Af = 3843 in2 = 2.48 m2
V = 60 MPH = 26.8 m/s

Fd = 481 N

POWER - Fd * V

P = 12.9 kW

Getting actual tire RR data is hard but Wikipedia has a list that includes Bridgestones at around an astonishingly low 0.00615. If we use this value we get:

P = 11.6 kW.

I personally see about 9 kW of consumption rolling at 60 MPH. That's about a 22% difference between actual and calculated.

Hope that helps.

9kW seems rather low.

Did you do it in both directions over the same stretch of road? What was the temperature - the air density is pretty much inversely proportional; to absolute temperature.

9kW is about 6.6miles/kWh - I think it is more like 5.4kWh/mil @60mph. This works out to 11.1kW, similar to your calculation.

I think you would get a more accurate measurement by resetting the trip meter, doing a few miles in one direction along a piece of road and taking the kWh reading. The repeating in the other direction and averaging.

kevin

kevin said:

9kW seems rather low.

Did you do it in both directions over the same stretch of road? What was the temperature - the air density is pretty much inversely proportional; to absolute temperature.

9kW is about 6.6miles/kWh - I think it is more like 5.4kWh/mil @60mph. This works out to 11.1kW, similar to your calculation.

I think you would get a more accurate measurement by resetting the trip meter, doing a few miles in one direction along a piece of road and taking the kWh reading. The repeating in the other direction and averaging.

kevin

Click to expand...

Yes I made a point of doing both directions. Temperatures have varied but anywhere between 65-85 F has been my experience in such observations.

I've been averaging 5.5 miles/kWh for the last 16000 miles. I know I've done better at steady state as I reset my trip once or twice during the early days of ownership and hit mid 6's then. It's doable.

nozferatu said:

P = 12.9 kW

Getting actual tire RR data is hard but Wikipedia has a list that includes Bridgestones at around an astonishingly low 0.00615. If we use this value we get:

P = 11.6 kW.

I personally see about 9 kW of consumption rolling at 60 MPH. That's about a 22% difference between actual and calculated.

Hope that helps.

Click to expand...

Welcome back from your vacation.

1) Your calculations with vehicle weight doesn't include the cargo and passengers.

2) There's no correction for air temperature in the air density calculation

This is what we observe @ 62mph / 100km ground speed at sea level to 1000 feet air density (ground speed can be different than the speedometer readout). Our data is on par to your calculated data, and significantly different than your observed data.

GM / Chevrolet
2014 Spark EV - 5 miles per kWh (200 wattHours per mile) = 12.4kW

2015 Spark EV - 5 miles per kWh (200 wattHours per mile) = 12.4kW

Chaconzies said:

Click to expand...

No image man...it just says image.

newwaysys said:

...

The reason the Spark has a relatively high Cd compared to a Prius(.25) has to do with cooling requirements for battery and motor.

Click to expand...

Unlikely - the cooling needed for the Spark would be less than the Prius and and as you say the Spark has an active grille.

The main difference is probably the shorter length of the Spark constraining the aerodynamics.

kevin

newwaysys said:

Iknow the CD is ~.33. What is the cross sectional area? What is the simple formula for using these numbers to derive HP vs speed? Forget Reynolds numbers, I'm not going supersonic. I have seen numbers published for autos which give the HP needed to overcome drag at 55mph. These are typically around 5 HP. They also give HP required to overcome rolling resistance.
http://mobilenumbertrackr.com/how-to-remove-whatsapp-blue-tick.aspx
Another question: How much reduction in drag does the active grille provide?

The reason the Spark has a relatively high Cd compared to a Prius(.25) has to do with cooling requirements for battery and motor.

Click to expand...

Kevin is correct.

Frontal surface area and trailing drag are the major factors in calculating F for a vehicle at speed...the force required to travel at a certain velocity within a certain velocity range. As speed increases over a certain point, other aerodynamics issues come into play, viscosity, boundary layers. etc.

The reason why the Pruis Cd is so much lower than the Spark's is mostly due to the rear end and many small touches that are not present on the Spark. The MB CLA 250 also has one of the lowest Cds in the industry at 0.23 (but that's under debate as some sources have tested it to be a lot more). It maintains laminar flow across the majority of its body and rear flow separation is smooth.

In contrast the Spark is not only turbulent at the rear end due to an abrupt change in rear end shape, but also taller. The frontal surface area is large as well. But many manufacturers these days add touches to keep flow laminate as long as possible and avoid high pressure points by using designs such as bug-eye headlights to direct flow around the side mirrors and a smooth underfloor pan that allows for smooth air flow under the car. Plus many cars have diffuser rakes to allow for smooth separation of airflow at the rear.

The active air grill has a purpose that many may not realize...it's not only to reduce drag but also increases down-force on the front axles for high speed stability. It redirects airflow up and around the hood to increase the down force. It probably isn't very much but you're likely to see about 15-20lbs of down force due to shutting of the grills at around 70 MPH.

The Prius design mimics an airfoil basically. The upper part does at least and an airfoil is the one of the most efficient shapes aerodynamically. It also incorporates lots of small features that reduce static pressure points such as directly airflow around the tires in the rear and front, smooth interfacing for the body and windshield, the side mirrors are well offset from the body, etc etc.

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. 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.

nozferatu said:

The active air grill has a purpose that many may not realize...it's not only to reduce drag but also increases down-force on the front axles for high speed stability. It redirects airflow up and around the hood to increase the down force. It probably isn't very much but you're likely to see about 15-20lbs of down force due to shutting of the grills at around 70 MPH.

Click to expand...

Oh wow that's really interesting, I had no idea this happened... and I regularly drive at 70 mph :lol:

I looked it up and not only does it help stability but also increases range

http://media.chevrolet.com/media/us/en/chevrolet/vehicles/spark-ev/2015.html

"Aero refinements, unique wheels and tires and active shutter system on the grille opening help extend the Spark EV’s range....Unique chrome upper two-tier grille is closed to reduce airflow...Active shutter system controls airflow through the lower intake open"

Chaconzies said:

nozferatu said:

The active air grill has a purpose that many may not realize...it's not only to reduce drag but also increases down-force on the front axles for high speed stability. It redirects airflow up and around the hood to increase the down force. It probably isn't very much but you're likely to see about 15-20lbs of down force due to shutting of the grills at around 70 MPH.

Click to expand...

Oh wow that's really interesting, I had no idea this happened... and I regularly drive at 70 mph :lol:

I looked it up and not only does it help stability but also increases range

http://media.chevrolet.com/media/us/en/chevrolet/vehicles/spark-ev/2015.html

"Aero refinements, unique wheels and tires and active shutter system on the grille opening help extend the Spark EV’s range....Unique chrome upper two-tier grille is closed to reduce airflow...Active shutter system controls airflow through the lower intake open"

Click to expand...

Yes of course that is 100% correct. They reduce static pressure build up at the front and re direct the flow. :mrgreen: