Drag Force Calculations

Paul Hobson <[email hidden]> wrote in news:dj1hnf$75p$1@news-
int.gatech.edu:

Quoted message said:

In going over some old hydraulics notes for a current class, I stumbled
across a problem I worked calculating the drag force and power output
required for a cyclist at various headwinds. I threw it all into
MathCad really fast so I could share. I added some graphs too.

If you're awesome and use the metric system:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_SI.htm

If you prefer US units:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_us.htm

Any thoughts? Gross errors?

\\paul

I'm not going to question your math, but the power values look awfully high
to me. I frequently ride at 20 mph into a 10 mph wind, and my CD is way
higher than racing cyclist. And that's not counting the "inefficiency" of
the bike, like getting the wheels to centripitally accelerate. In other
words, I really don't think I'm putting out 450 - 500 watts in a real
situation. If I am, find me a trireme, I'd love to go on a nice cruise 😉

--ag

Andy Gee said:

Paul Hobson <[email hidden]> wrote in news:dj1hnf$75p$1@news-
int.gatech.edu:

Quoted message said:

In going over some old hydraulics notes for a current class, I stumbled
across a problem I worked calculating the drag force and power output
required for a cyclist at various headwinds. I threw it all into
MathCad really fast so I could share. I added some graphs too.

If you're awesome and use the metric system:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_SI.htm

If you prefer US units:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_us.htm

Any thoughts? Gross errors?

\\paul

I'm not going to question your math, but the power values look awfully high
to me. I frequently ride at 20 mph into a 10 mph wind, and my CD is way
higher than racing cyclist. And that's not counting the "inefficiency" of
the bike, like getting the wheels to centripitally accelerate. In other
words, I really don't think I'm putting out 450 - 500 watts in a real
situation. If I am, find me a trireme, I'd love to go on a nice cruise 😉

--ag

Hmm...it was an example problem worked in class -- originally in US
units. In that MathCad worksheet, I got the same answer as the
professor, which was 0.047 hp for the tail wind and 0.422 hp for the
head wind, respectively. According to both MathCad, my HP-48G+
calculator <heart>, and myself with conversion factors, those figures
roughly translate to 35.1 W and 315.5 W (I rounded the velocities to
nice even numbers so the two versions don't exactly translate).

The situation at you mention -- going at 20 mph with a 10 mph headwind
-- would correspond to an output of 315.5 W, which is somewhat lower
than the 450 W to 500 W range that you mention. Yes, it does seem high.
But 20 mph with a 10 mph headwind is not an easy situation. Quite
impressive, really. Lastly, keep in mind that the SI chart's x-axis is
in kph (kilometers per hour).

....

Any better?
--
Paul M. Hobson
Georgia Institute of Technology
..:change the words to numbers
if you want to reply to me:.

Paul Hobson said:

Any thoughts? Gross errors?

How come it requires .2 hp to go zero MPH? Shouldn't it require 0 HP?

Rich said:

Paul Hobson said:

Any thoughts? Gross errors?

How come it requires .2 hp to go zero MPH? Shouldn't it require 0 HP?

In the second graph (right?), 0 mph is the velocity of the *air*
relative to the *ground*. Thus, the air would be moving at 20 mph
relative to the cyclist.

--
Paul M. Hobson
Georgia Institute of Technology
..:change the words to numbers
if you want to reply to me:.

Paul Hobson said:

In going over some old hydraulics notes for a current class, I stumbled
across a problem I worked calculating the drag force and power output
required for a cyclist at various headwinds. I threw it all into
MathCad really fast so I could share. I added some graphs too.

If you're awesome and use the metric system:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_SI.htm

If you prefer US units:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_us.htm

Any thoughts? Gross errors?

\\paul

These calculators are all over the net, why not cross check against them?

Peter Cole said:

Paul Hobson said:

In going over some old hydraulics notes for a current class, I
stumbled across a problem I worked calculating the drag force and
power output required for a cyclist at various headwinds. I threw it
all into MathCad really fast so I could share. I added some graphs too.

If you're awesome and use the metric system:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_SI.htm

If you prefer US units:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_us.htm

Any thoughts? Gross errors?

\\paul

These calculators are all over the net, why not cross check against them?

Oh, I had no idea. [googles]

--
Paul M. Hobson
Georgia Institute of Technology
..:change the words to numbers
if you want to reply to me:.

Paul Hobson said:

In going over some old hydraulics notes for a current class, I stumbled
across a problem I worked calculating the drag force and power output
required for a cyclist at various headwinds. I threw it all into
MathCad really fast so I could share. I added some graphs too.

If you're awesome and use the metric system:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_SI.htm

If you prefer US units:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_us.htm

Any thoughts? Gross errors?

\\paul

What are the same values for temperatures other than ~60 F? I bike
at temperatures from -15 to 90. Drag force is really much more
noticeable at higher density -- although maybe it's because I
present a larger cross-section to the wind.

Scott

Scott said:

Paul Hobson said:

In going over some old hydraulics notes for a current class, I
stumbled across a problem I worked calculating the drag force and
power output required for a cyclist at various headwinds. I threw it
all into MathCad really fast so I could share. I added some graphs too.

If you're awesome and use the metric system:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_SI.htm

If you prefer US units:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_us.htm

Any thoughts? Gross errors?

\\paul

What are the same values for temperatures other than ~60 F? I bike
at temperatures from -15 to 90. Drag force is really much more
noticeable at higher density -- although maybe it's because I
present a larger cross-section to the wind.

Drag coefficients are independent of the fluid in which bodies are
submerged. To account for different temperatures, the density simply
needs to be changed using the Ideal Gas Law:

density = (P*M)/(R*T)
with
P = pressure (kPa or lbf/ft^2)
M = molecular weight of air = 28.97 kg/kmol = lbm/lbmol
R = 8.314 kJ/kmol*K = 1545 lbf/lbmol * degrees Rankine
T = temperature in Kelvins or degrees Rankine as appropriate

Since the power output is directly proportional to the density, simply
multiply the final answers on my sheet by the ratio of your calculated
density over the one I used.

I also found this:

Area (ft^2) C_D
upright commuter 5.5 1.1
racing 3.9 0.88
drafting 3.9 0.50
streamlined* 5.0 0.12

* the illustration for this is a very simple silhouette of a recumbent
with what I guess us some sort of cage that they use in those
human-powered speed competitions. it doesn't really explain the
values at all.
--
Paul M. Hobson
Georgia Institute of Technology
..:change the words to numbers
if you want to reply to me:.

Paul Hobson said:

Scott said:

Paul Hobson said:

In going over some old hydraulics notes for a current class, I
stumbled across a problem I worked calculating the drag force and
power output required for a cyclist at various headwinds. I threw it
all into MathCad really fast so I could share. I added some graphs too.

If you're awesome and use the metric system:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_SI.htm

If you prefer US units:
http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_us.htm

Any thoughts? Gross errors?

\\paul

What are the same values for temperatures other than ~60 F? I bike
at temperatures from -15 to 90. Drag force is really much more
noticeable at higher density -- although maybe it's because I
present a larger cross-section to the wind.

Drag coefficients are independent of the fluid in which bodies are
submerged. To account for different temperatures, the density simply
needs to be changed using the Ideal Gas Law:

density = (P*M)/(R*T)
with
P = pressure (kPa or lbf/ft^2)
M = molecular weight of air = 28.97 kg/kmol = lbm/lbmol
R = 8.314 kJ/kmol*K = 1545 lbf/lbmol * degrees Rankine
T = temperature in Kelvins or degrees Rankine as appropriate

Since the power output is directly proportional to the density, simply
multiply the final answers on my sheet by the ratio of your calculated
density over the one I used.

I also found this:

Area (ft^2) C_D
upright commuter 5.5 1.1
racing 3.9 0.88
drafting 3.9 0.50
streamlined* 5.0 0.12

* the illustration for this is a very simple silhouette of a recumbent
with what I guess us some sort of cage that they use in those
human-powered speed competitions. it doesn't really explain the values
at all.

Very interesting. I really do find it much more difficult
to bike in the ~10% denser air of winter than summer and
have always assumed it's because of greater drag in the
denser air, rather than the effect of density on the power
ouput. Incidentally, I guess I'm the upright commuter --
and in winter with bulky clothes, the cross-section is a
lot higher. So it's a combination of the two.

Scott

Scott said:

Paul Hobson said:

Scott said:

Paul Hobson wrote:

> In going over some old hydraulics notes for a current class, I
> stumbled across a problem I worked calculating the drag force and
> power output required for a cyclist at various headwinds. I threw
> it all into MathCad really fast so I could share. I added some
> graphs too.
>
> If you're awesome and use the metric system:
> http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_SI.htm
>
> If you prefer US units:
> http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_us.htm
>
> Any thoughts? Gross errors?
>
> \\paul

What are the same values for temperatures other than ~60 F? I bike
at temperatures from -15 to 90. Drag force is really much more
noticeable at higher density -- although maybe it's because I
present a larger cross-section to the wind.

Drag coefficients are independent of the fluid in which bodies are
submerged. To account for different temperatures, the density simply
needs to be changed using the Ideal Gas Law:

density = (P*M)/(R*T)
with
P = pressure (kPa or lbf/ft^2)
M = molecular weight of air = 28.97 kg/kmol = lbm/lbmol
R = 8.314 kJ/kmol*K = 1545 lbf/lbmol * degrees Rankine
T = temperature in Kelvins or degrees Rankine as appropriate

Since the power output is directly proportional to the density, simply
multiply the final answers on my sheet by the ratio of your calculated
density over the one I used.

I also found this:

Area (ft^2) C_D
upright commuter 5.5 1.1 racing 3.9 0.88
drafting 3.9 0.50
streamlined* 5.0 0.12

sorry about the crappy formatting -- it looked better when I typed it up.

Quoted message said:

Quoted message said:

* the illustration for this is a very simple silhouette of a recumbent
with what I guess us some sort of cage that they use in those
human-powered speed competitions. it doesn't really explain the
values at all.

Very interesting. I really do find it much more difficult
to bike in the ~10% denser air of winter than summer and
have always assumed it's because of greater drag in the
denser air

you're right, it is.

Quoted message said:

rather than the effect of density on the power
ouput.

and you are right there too!

Quoted message said:

Incidentally, I guess I'm the upright commuter --
and in winter with bulky clothes, the cross-section is a
lot higher. So it's a combination of the two.

The denser air increases the drag force, which /then/ increases the
required power output. So, AFAIK, you were correct in your initial
assessment.

Drag Force is proportional to air density.
Power output is proportional to drag force, therefore
Power output is proportional to air density. make sense?

--
Paul M. Hobson
Georgia Institute of Technology
..:change the words to numbers
if you want to reply to me:.

Paul Hobson said:

Scott said:

Paul Hobson said:

Scott wrote:

> Paul Hobson wrote:
>
>> In going over some old hydraulics notes for a current class, I
>> stumbled across a problem I worked calculating the drag force and
>> power output required for a cyclist at various headwinds. I threw
>> it all into MathCad really fast so I could share. I added some
>> graphs too.
>>
>> If you're awesome and use the metric system:
>> http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_SI.htm
>>
>> If you prefer US units:
>> http://www.prism.gatech.edu/~gtg611a/bike_calcs/drag_net_us.htm
>>
>> Any thoughts? Gross errors?
>>
>> \\paul
>
>
>
>
>
> What are the same values for temperatures other than ~60 F? I bike
> at temperatures from -15 to 90. Drag force is really much more
> noticeable at higher density -- although maybe it's because I
> present a larger cross-section to the wind.

Drag coefficients are independent of the fluid in which bodies are
submerged. To account for different temperatures, the density simply
needs to be changed using the Ideal Gas Law:

density = (P*M)/(R*T)
with
P = pressure (kPa or lbf/ft^2)
M = molecular weight of air = 28.97 kg/kmol = lbm/lbmol
R = 8.314 kJ/kmol*K = 1545 lbf/lbmol * degrees Rankine
T = temperature in Kelvins or degrees Rankine as appropriate

Since the power output is directly proportional to the density,
simply multiply the final answers on my sheet by the ratio of your
calculated density over the one I used.

I also found this:

Area (ft^2) C_D
upright commuter 5.5 1.1 racing 3.9 0.88
drafting 3.9 0.50
streamlined* 5.0 0.12

sorry about the crappy formatting -- it looked better when I typed it up.

Quoted message said:

Quoted message said:

* the illustration for this is a very simple silhouette of a
recumbent with what I guess us some sort of cage that they use in
those human-powered speed competitions. it doesn't really explain
the values at all.

Very interesting. I really do find it much more difficult
to bike in the ~10% denser air of winter than summer and
have always assumed it's because of greater drag in the
denser air

you're right, it is.

Quoted message said:

rather than the effect of density on the power
ouput.

and you are right there too!

Oops -- I read 'drag coefficients are independent of fluid'
as 'drag is independent of fluid' -- which didn't make sense.

Never mind!!!

scott