Power = Speed Cubed; the Propeller Rule

BretCahill said:

According to the propeller rule, a boat needs eight times times more power to double speed, 27
times more power to triple speed.

Does this hold for air?

If so, it takes almost twice as much power to time trial at 30 mph as 24 mph.

analyticcycling.comForcesPower Page.htmlOpen ↗

Quoted post said:

Originally posted by Bretcahill
According to the propeller rule, a boat needs eight times times more power to double speed, 27 times
more power to triple speed.

Does this hold for air?

If so, it takes almost twice as much power to time trial at 30 mph as 24 mph.

Bret Cahill

No.

Fluidic resistances such as water and wind on a bike or water-craft increase in proportion to the square of velocity.

Rolling resistances on a bike increase linearly proportional to velocity.
On a bike, the wind resistance is typically about 80% of the total resistance at about 18 mph. If you extrapolated this relationship to 24 mph, 84.3% of total bike resistance is wind resistance.
At 30 mph you would use 1.51 times as much power as at 24 mph.
at 34.9 mph you would TT with the example bike at double the power of a 24 mph speed.

Watercraft face all their moving resistance in water + wind resistance-resistances that increase in proportion to the velocity square virtually nothing incerasing linearly with velocity.
Energy is lost out from the propeller propulsion system pushing the water back.
Hydroplane racers often say they loose half the drivetrain energy in the propeller driven spray. Its not apparent to me why they loose that much power from the propeller, but that statement exactly coincides with the 8x propeller rule you cited when you multiply by two the change in power needed to overcome the watercrafts fluidic resistance.

Robert’s cited link is appropriate for bikes.

I think the power required is proportional to the square of the (net) velocity
156.25% from 24 to 30

nick

"BretCahill" <[email hidden]> wrote in message
"]news:[email hidden]... According to the propeller rule, a boat needs
eight times times more power to double speed, 27 times more power to triple speed.

Does this hold for air?

If so, it takes almost twice as much power to time trial at 30 mph as 24 mph.

Bret Cahill

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

Quoted message said:

According to the propeller rule, a boat needs eight times times more power to double speed, 27
times more power to triple speed.

Does this hold for air?

The short answer is yes, because the force required to overcome aerodynamic drag increases as the
square of the speed, and power is speed times force.

Quoted message said:

If so, it takes almost twice as much power to time trial at 30 mph as 24 mph.

Bret Cahill

Nicholas & Domino said:

I think the power required is proportional to the square of the (net) velocity
156.25% from 24 to 30

nick

"BretCahill" <[email hidden]> wrote in message
"]news:[email hidden]... According to the propeller rule, a boat needs
eight times times more power to double speed, 27 times more power to triple speed.

Does this hold for air?

If so, it takes almost twice as much power to time trial at 30 mph as 24 mph.

Bret Cahill

The force required goes roughly with the square of the speed thus the power goes with the cube of
the speed.

"dr. dave" <[email hidden]> wrote in message
news:<[email hidden]>... <snip>

Quoted message said:

The force required goes roughly with the square of the speed thus the power goes with the cube of
the speed.

In other words, streamlining pays big dividends. Take a look at the bikes running at the World Human
Powered Speed Challenge: wisil.recumbents.comresultsmonday.htmOpen ↗ and check
out their speeds: wisil.recumbents.comresults.htmOpen ↗

Jeff

Jeff Wills said:

Quoted message said:

The force required goes roughly with the square of the speed thus the power goes with the cube
of the speed.

In other words, streamlining pays big dividends. Take a look at the bikes running at the World
Human Powered Speed Challenge: wisil.recumbents.comresultsmonday.htmOpen ↗
and check out their speeds: wisil.recumbents.comresults.htmOpen ↗

Actually just the opposite. The higher the exponent (3), the less difference streamlining makes. If
you halve the drag coefficient you get only the cube root of two increase in speed (1.26). With
linear power it would double.
--
Ron Hardin [email hidden]

On the internet, nobody knows you're a jerk.

"Ron Hardin" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

Jeff Wills said:

Quoted message said:

The force required goes roughly with the square of the speed thus the power goes with the cube
of the speed.

In other words, streamlining pays big dividends. Take a look at the bikes running at the World
Human Powered Speed Challenge: wisil.recumbents.comresultsmonday.htmOpen ↗
and check out their speeds: wisil.recumbents.comresults.htmOpen ↗

Actually just the opposite. The higher the exponent (3), the less

difference

Quoted message said:

streamlining makes. If you halve the drag coefficient you get only the

cube root

Quoted message said:

of two increase in speed (1.26). With linear power it would double.

I guess you could look at it that way - but since we know a priori that drag in a fluid medium
increases as a square of the velocity (such that power increases as a cubic function), the statement
"streamlining pays big dividends" implies that air (or water) resistance is the dominant force to be
overcome. Systems in which the power requirement increases as a linear function of velocity are
obviously those in which velocity is low (e.g., climbing a steep hill).

Andy Coggan

Andy Coggan said:

Quoted message said:

Actually just the opposite. The higher the exponent (3), the less

difference

Quoted message said:

streamlining makes. If you halve the drag coefficient you get only the

cube root

Quoted message said:

of two increase in speed (1.26). With linear power it would double.

I guess you could look at it that way - but since we know a priori that drag in a fluid medium
increases as a square of the velocity (such that power increases as a cubic function), the
statement "streamlining pays big dividends" implies that air (or water) resistance is the dominant
force to be overcome. Systems in which the power requirement increases as a linear function of
velocity are obviously those in which velocity is low (e.g., climbing a steep hill).

In some systems, a constant speed is wanted, eg. clock escapements, and I guess door closers (I
don't know how these work), regardless of force. I think these have a very high exponent in the drag
law, the clock in effect, and the door closer I don't know about.
--
Ron Hardin [email hidden]

On the internet, nobody knows you're a jerk.