the terrible (?) truth about tailboxes

Paul Worden screv:

"It's claimed by the builders of the M5 trike that their tailbox reduces energy requirements by 28%
All the figures that I've seen suggest that a tailbox only increases average speed by about 2 - 5
kph ( 1 - 3 mph) How does an energy saving of nearly 30 percent only create an added 2 kph?"

Because power required increases by the square of velocity. (or is it cube??). 1.1 * 1.1 = 1.21.
1.1*1.1*1.1=1.33.

See????

Tom

Quoted message said:

Thank you Tom.....1.1 * 1.1 = 1.21. 1.1*1.1*1.1=1.33.

that's much clearerer (!)

it makes me glow with admiration for a wedgie sprinter that can top 64 kph......

Paul W ...Swift by name, but obviously not by nature.....

"Tom Blum" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

Paul Worden screv:

"It's claimed by the builders of the M5 trike that their tailbox reduces energy requirements by
28% All the figures that I've seen suggest that a tailbox only increases

average

Quoted message said:

speed by about 2 - 5 kph ( 1 - 3 mph) How does an energy saving of nearly 30 percent only create
an added 2

kph?"

Quoted message said:

Because power required increases by the square of velocity. (or is it cube??). 1.1 * 1.1 = 1.21.
1.1*1.1*1.1=1.33.

Drag force goes as the square of the velocity, power as the cube.

Quoted message said:

See????

Yep.

Fred

Quoted message said:

Could some experienced bent designer/rider add some light to this.

It's claimed by the builders of the M5 trike that their tailbox reduces energy requirements by 28%
All the figures that I've seen suggest that a tailbox only increases average speed by about 2 - 5
kph ( 1 - 3 mph) Tailboxes that I've attached to my MR Swift increase my average speed over a
hilly 25 kms (15 miles) by about 2 kph and my max rolldown on a known short hill from 58 to 63 kph
(35 - 38 mph.)

How does an energy saving of nearly 30 percent only create an added 2 kph? Aaaarghhhh...... maths
was never my strong area.....

Paul Worden - MR Swift

Hi Paul

I'll give it a try.

The power required to overcome rolling resistance and aero resistance can be viewed as two
separate figures, and added together at a given speed.

Rolling resistance force, and the power to overcome it, varies directly with your speed... if
you go twice as fast, it takes twice the power.

Aero drag FORCE varies as the square of your speed, so if you go twice as fast, you have four
times the aero drag (aero drag force varies as speed squared)

Distance traveled comes into the equation for power though (P= Force X Distance/Time) so
going twice as fast requires eight times the power (power to overcome aero drag varies as the
speed cubed)

As the speeds approach those in the M5 SRM measurements (43-46km/hr) the aero drag force
starts to dominate the equation, and very small increases in speed result from large
decreases in aero drag or large increases in power.

Hope this helped.

Rich Pinto
Bacchetta Bicycles

RCPINTO said:

... Rolling resistance force, and the power to overcome it, varies directly with your speed... if
you go twice as fast, it takes twice the power....

This will almost never be true. Riding faster will create more heat due to the flexure of the tire
casing and friction between the casing and inner tube. The temperature increase will change the air
pressure and/or the rolling diameter and/or width of the tire. The elastic modulus and coefficient
of restitution of the elastomers in the tire and inner tube will also likely very significantly with
temperature.

Tom Sherman - Recumbent Pedant

Arguing with an engineer is like mud wrestling with a pig... You soon find out the pig likes
it! - Unknown

Tom Sherman said:

will also likely very significantly with temperature.

vary

[email hidden] (RCPINTO) wrote in message news:<[email hidden]>...

Quoted message said:

Rolling resistance force, and the power to overcome it, varies directly with your speed... if
you go twice as fast, it takes twice the power.

Rich,

Don't you mean:

Rolling resistance force varies directly with your speed and the power to overcome it varies as the
square of your speed.

Len Thunberg

Aerodynamic resistance doesn't necessarily increase by a factor of 4 with an increase in speed. It
really can't be calculated without actual testing, using a full-sized model or actual working
vehicle. This is because different airframes have variations in how well they perform at certain
speeds. Some airframes have a terminal velocity that is lower than others, because the airflow
becomes turbulent enough at that speed to greatly raise the drag. Other designs might allow a smooth
airflow to be maintained at much greater speeds. Some designs might have poor airflow
characteristics at lower speeds, but when pushed faster the airflows might smooth out into more
laminar patterns. The formulas that some claim can be used to calculate drag on a proposed design,
are theoretical only. Only when proven designs are only slighly changed, can these theories come
close to matching actual performance.

The reason the Boeing engineers may have been able to design the 777 completely by computer, is
because they had previously designed and proven the 757 and 767 in the old-fashioned way and
had all the data from them to feed their computers.

That 2 or 3 kph increase in speed from a tailbox sounds pretty good to me. I've worked hard
over designs to squeeze out far less extra speed than that.

Steve McDonald

rotofool said:

[email hidden] (RCPINTO) wrote in message news:<[email hidden]>...

Quoted message said:

Rolling resistance force, and the power to overcome it, varies directly with your speed... if
you go twice as fast, it takes twice the power.

Don't you mean:

Rolling resistance force varies directly with your speed and the power to overcome it varies as
the square of your speed.

No, Rich had it right. Rolling resistance, i.e. tires and bearings, is proportional to speed. It is
only aerodynamic forces that increase at a higher rate.
--

John Foltz --- O _ Baron --- _O _ V-Rex 24/63 --- _\\/\-%)
_________(_)`=()___________________(_)= (_)_____

John Foltz said:

rotofool said:

[email hidden] (RCPINTO) wrote in message
news:<[email hidden]>...

Quoted message said:

Rolling resistance force, and the power to overcome it, varies directly with your speed... if
you go twice as fast, it takes twice the power.

Don't you mean:

Rolling resistance force varies directly with your speed and the power to overcome it varies as
the square of your speed.

No, Rich had it right. Rolling resistance, i.e. tires and bearings, is proportional to speed. It
is only aerodynamic forces that increase at a higher rate.

While I'm sure Rich understands it perfectly, he didn't type it quite right. Rolling
resistance force is nearly a constant, and since power is force times velocity, power to
overcome rolling resistance is proportional to speed. As he stated, if you go twice as fast,
it takes twice the power.

Dave Lehnen

John Foltz <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

rotofool said:

[email hidden] (RCPINTO) wrote in message
news:<[email hidden]>...

Quoted message said:

Rolling resistance force, and the power to overcome it, varies directly with your speed... if
you go twice as fast, it takes twice the power.

Don't you mean:

Rolling resistance force varies directly with your speed and the power to overcome it varies as
the square of your speed.

No, Rich had it right. Rolling resistance, i.e. tires and bearings, is proportional to speed. It
is only aerodynamic forces that increase at a higher rate.

John,

If you'll reread my post you'll see that I said rolling resistance is proportional to speed. My
point was that the power required to overcome that resistance varies as the square of speed, power
being a constant times resistance times speed.

Len Thunberg

Steve MacDonald wrote;

Quoted message said:

Aerodynamic resistance doesn't necessarily increase by a factor of 4 with an increase in
speed. It really can't be calculated without actual testing, using a full-sized model or
actual working vehicle. This is because different airframes have variations in how well they
perform at certain speeds. Some airframes have a terminal velocity that is lower than others,
because the airflow becomes turbulent enough at that speed to greatly raise the drag. Other
designs might allow a smooth airflow to be maintained at much greater speeds. Some designs
might have poor airflow characteristics at lower speeds, but when pushed faster the airflows
might smooth out into more laminar patterns.

Steve

The difference between airplanes (Cd's under .1) and bluff bodies like unfaired bicycles (Cd's
from ~.5 to about .9) is that almost all of the drag on airplanes is from skin friction, and
almost all of the drag on unfaired bicycles drag is due to pressure drag.

Cd's are just a measure of the streamlining of any object, per unit of frontal area. The lower
the Cd, the more streamlined the object.

Airplanes also have much higher speeds, and complicated laminar/turbulent flow control problems
under various yaws, lifts, etc. In general, a much more complicated problem than the normal
turbulent and separating air flow of unfaired bicycles.

The range of speeds of interest for bicycle aero drag calculation's is also much slower at
20-35 MPH, and in a stable Cd range.

Cd's of various objects can change based on speed, size, and fluid viscosity (which the
dimensionless "Reynolds number" describes) and suddenly drop by a factor of four over a very
small range of velocities, as air is tripped into turbulence and reduces the separated area
(low pressure) behind the object.

I've never seen bicycle Cd's change over the normal range of wind tunnel velocities though, so
the aero drag force does scale with the velocity squared for the normal range of interest.

Rich Pinto
Bacchetta Bicycles

[email hidden] (Steve McDonald) wrote in message
news:<[email hidden]>...

Quoted message said:

The reason the Boeing engineers may have been able to design the 777 completely by computer,
is because they had previously designed and proven the 757 and 767 in the old-fashioned way
and had all the data from them to feed their computers.

OT here, but... 15 years ago NASA engineers were able to calculate (accurately) the aerodynamics of
an airframe. Only trouble was it took several days on a Cray 2 to get the results. Nowadays I
imagine that a few hours on a modern supercomputer will do the same thing. Really, computation fluid
dynamics (CFD) was a solved problem years ago. The only reason for looking at the old data is to
double check the results of the simulations.

-- archer

Weren't these the same folks who divided inches by centimeters on the way to Mars. bill, where is
that stinkin telescope, g

archer said:

OT here, but... 15 years ago NASA engineers were able to calculate (accurately) the aerodynamics
of an airframe. Only trouble was it took several days on a Cray 2 to get the results. -- archer

[email hidden] (RCPINTO) wrote in message news:<[email hidden]>...

Quoted message said:

Quoted message said:

RCPINTO said:

... Rolling resistance force, and the power to overcome it, varies

directly

Quoted message said:

Quoted message said:

with your speed... if you go twice as fast, it takes twice the power....

This will almost never be true. Riding faster will create more heat due to the flexure of the
tire casing and friction between the casing and inner tube. The temperature increase will change
the air pressure and/or the rolling diameter and/or width of the tire. The elastic modulus and
coefficient of restitution of the elastomers in the tire and inner tube will also likely very
significantly with temperature.

Tom Sherman - Recumbent Pedant

Arguing with an engineer is like mud wrestling with a pig... You soon find out the pig likes it!
- Unknown

To the nearest watt of power, and for the sake of explaining it to someone who was having a
hard time grasping the concepts, the power to overcome rolling resistance is directly
proportional to speed.

And now for the "mud wrestling with a pig" portion of the explanation ;<😉...yes, there are
very small second order effects to bicycle tire rolling resistance which is described by this
equation;

Crr= Cro + (Crv X V)

or, the total rolling resistance= base Crr + (a VERY small # times the velocity in M/S)

The significance of this speed dependent rolling resistance effect for bicycle tires can be
judged by its lack of mention in almost every rolling resistance measurement study of
bicycle tires you can find, with only one exception that I can find, in "Bicycling
Science", where it is briefly mentioned.

As far as temperature effects on rolling resistance, of course changes in the tire and tube
temperature, and the increases in tire pressure will cause changes in Crr. But all else being
equal, at a given temperature and tire pressure, to a very close approximation...rolling
resistance power is proportional to speed.

Rich Pinto
Bacchetta Bicycles

I'm going to take a shower now!! - Unknown...after mud wrestling :<😉

Hey 'M&M(Marked Man) Rich, Are we having fun yet? Emmett

a&b <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

Weren't these the same folks who divided inches by centimeters on the way to Mars. bill, where is
that stinkin telescope, g

Nope. That was the, ahem, fine engineers down at Lockheed in Colorado Springs. And it was ft-lbs/sec
vs NM/sec, IIRC. CFD work is done at Moffitt NAS in Sunnyvale, CA. -- a