Aerodynamic Streamlining Template: Part-C

[Bicycle Bob]

Havn't you guys ever wondered why the experts use giant computers for such estimates, and then check their work with a wind tunnel?

[aerohead]

Originally Posted by freebeard

I think The Template is ideal in theory only, but I will ask: Do you think the disparity from 30 to 50% is more significant than what's at 80%? It certainly involves more cross-sectional area.

aerohead — Can you comment on 'phantom tail' truncations and the reflex curve add-on to the Baby Template? I forget, was it same-same with or without it?

Whoa! Simul-post. I'll have to go back and read that.

*Most of the gains occur early in the boat-tailing.
*Additional elongation suffers diminishing returns.
*Fachsenfeld and Kamm,at the FKFS, considered that a 'practical' length car would be truncated at 50% frontal area,to allow a motorist to navigate urban environments and hazards.
*An extensible tail would allow additional drag reduction on the open highway,when aero would be most important.(like Mercedes has done recently with their concept car).
*The FKFS' best,full-tailed,knife-edged body came in at Cd 0.12,as with Walter Lay's 1933 'car.'
*Unfortunately for us,they never tested this 'ideal' body with a truncated tail at 50% frontal area.
*The Template came in at Cd 0.1487 truncated,and Cd 0.1209 as a long-tail.
*Whether the 18.7% drag reduction of the tail was worth the trouble would be up to the consumer,policy maker,etc..
-----------------------------------------------------------------------
*As to the phantom tail on Baby,the smoke indicated its presence.
*The von Mises,reflexion was a concession to extant DOT requirements for tail lights and license plate.(I wanted to simulate a legal road-going automobile)[ I suspect that she paid a price for losing plan taper of the boat tail]
*Using the Cambridge University Eco Racer CUER as a guide,it's conceivable that Baby would have measured in the neighborhood of Cd 0.11 with trailing knife-edges (as Layne commented on) and more closed-in wheel fairings (Goro Tamai).

[aerohead]

Originally Posted by Tesla

I've been pondering on this for a while now and I think we are coming to the limits of this process, as I understand it we have experimental data and experience which suggests a teardrop type shape with probably a bit less than the 2.5:1 ratio as being the ideal. The risk being that the penalties accrue much more rapidly below 2.5:1 than above if something goes awry. Then there is the real world where appendages change the story whether you are a fish, bird or motor vehicle.
Unless we can determine any other specific mathematical relationships, without extensive testing it is hard to determine what the ideal distribution along the curve would be.
My personal thoughts are that something of an S-curve might be the ideal where the angles accelerate rapidly through to 70-80% and then begin to taper back towards horizontal so that the converging air streams are aligned in a parallel manner. The Parametric equation had this characteristic, but any online search for teardrop equations will produce dozens of results, but which one is best?

*Hucho suggested that with fully-integrated wheels,we might achieve Cd 0.08.
*A streamlined body of revolution of L/D= 2.5 would be the basis.(Cd 0.04)
*These shapes are incapable of flow separation,the single most important consideration to aerodynamic streamlining.
*The 1983 Ford Probe-IV (not that unusual looking),as a 'camera' car would be Cd 0.137.This car could have been mass-produced in steel and glass in 1986,at no more cost than a Ford Escort.(36-month product cycles are nothing new)
*At Cd 0.137 we could have endeavored to go below that value,exploring the more organic shapes known to produce lower drag.
*We've lost untold $billions by not doing it.
*The automotive manufacturers may represent the only industry in which technological innovation means nothing in product design.

[aerohead]

Originally Posted by kach22i

If I read this correctly, good thoughts regarding cross winds.

This image below may help in visualization though it lacks the rounded C-pillars most of us would favor.

Forces and flow structures evolution on a car body in a sudden crosswind
https://www.sciencedirect.com/scienc...67610514000506



I could use a translation into Ecomodder English.

The 1985 Ford Probe-V was touted by Ford as to having superior crosswind stability.

[freebeard]

Originally Posted by Bicycle Bob

Havn't you guys ever wondered why the experts use giant computers for such estimates, and then check their work with a wind tunnel?

aerohead is too modest. He could have pointed to his adventures at Darko (so I will).

[gone-ot]

Originally Posted by Bicycle Bob

Havn't you guys ever wondered why the experts use giant computers for such estimates, and then check their work with a wind tunnel?

"Trust...but VERIFY!"

[Tesla]

I've been playing with the Power equation and have come up with a few interesting bits.
The original equation was simple y=ax^b which worked well for the purpose but was limited in adjustment, so I added a correction factor to subtract -cx and after playing with it came up with the following values for the CoEfficients:
0.31801x^-0.39103 - 0.05x, Power 2 equation, this matched the AS-II profile very well, just slightly above at 30-60% area. Using the same equation I tried to match up template angles 6.8-23 it matches ok, bit less 20-40%, then a bit more through mid range to catch up to the 23 at end, this one I called Power 2.2. I've left the original, Power 1, on the overlay as a comparison.



The fact that the Power 2 angles correlate quite well with the AS-II angles confirms the accuracy of the image, but it also confirms through 2.2 that the Template angles are more aggressive and result in less that 1.78 tail ratio.

I also looked at the rate of change of angles and also the calculated fall, the top two do not include Template as they require 100 data points, charts below:



The bottom two are based on 10 data points so I've included the template, the third chart shows how the Power 2 equations match the template much better than the original Power 1.
With the 4th chart, I've reduced the range at the start on both x&y axis because there was no significant distinctions at the start, all the interest was in the tail. As I had found interest in the "Rate of angle changes" I asked myself then what is the Rate of change the Rate of angle change, so kind of like a secondary derivative. The first thing that sticks out is the lines of the template which show an erratic direction whilst both the power equations continue to show a continuous rate change curve, like a typical ballistic trajectory. The other point of interest was that the Power 2 equations resulted in virtually identical values.

[aerohead]

Originally Posted by Tesla

I've been playing with the Power equation and have come up with a few interesting bits.
The original equation was simple y=ax^b which worked well for the purpose but was limited in adjustment, so I added a correction factor to subtract -cx and after playing with it came up with the following values for the CoEfficients:
0.31801x^-0.39103 - 0.05x, Power 2 equation, this matched the AS-II profile very well, just slightly above at 30-60% area. Using the same equation I tried to match up template angles 6.8-23 it matches ok, bit less 20-40%, then a bit more through mid range to catch up to the 23 at end, this one I called Power 2.2. I've left the original, Power 1, on the overlay as a comparison.



The fact that the Power 2 angles correlate quite well with the AS-II angles confirms the accuracy of the image, but it also confirms through 2.2 that the Template angles are more aggressive and result in less that 1.78 tail ratio.

I also looked at the rate of change of angles and also the calculated fall, the top two do not include Template as they require 100 data points, charts below:



The bottom two are based on 10 data points so I've included the template, the third chart shows how the Power 2 equations match the template much better than the original Power 1.
With the 4th chart, I've reduced the range at the start on both x&y axis because there was no significant distinctions at the start, all the interest was in the tail. As I had found interest in the "Rate of angle changes" I asked myself then what is the Rate of change the Rate of angle change, so kind of like a secondary derivative. The first thing that sticks out is the lines of the template which show an erratic direction whilst both the power equations continue to show a continuous rate change curve, like a typical ballistic trajectory. The other point of interest was that the Power 2 equations resulted in virtually identical values.

*In the literature for 3-D streamline bodies of revolution,the Bernoulli Equation-related velocity/pressure profile across the aft-body holds the position of authority with respect to drag.
*If the fineness ratio is below 2.5:1,the pressure recovery demands deceleration of the boundary layer,which is impossible,since it's already at rest against the body,initiating burble point,then full-blown, separation-induced turbulence and attendant pressure drag increasing drag above the minimum.
*If the fineness ratio exceeds 2.5:1,pressure drag due to separation is eliminated,however surface friction drag increases,and overall drag increases above the minimum.
*The 2.5:1 profile appears to embody the 'sweet-spot'.There's something about its aft-body profile especially representative of the bottom of the drag 'bucket',when plotted on a Cartesian L/D grid.Kinda like the 'Goldilocks' zone.
*Early airship research indicated 2.1:1 for a drag minimum,but this would be for enormous bodies,in which the sloughing turbulent boundary layer actually fills in part of the wake,following the hull wherever it goes,representing a larger 'phantom' fineness ratio.

[freebeard]

So in extreme cross-wind conditions, which has the advantage:

• Template stinger
• Dymaxion/blimp body
• flat or concave truncation

[aerohead]

Originally Posted by freebeard

So in extreme cross-wind conditions, which has the advantage:

• Template stinger
• Dymaxion/blimp body
• flat or concave truncation

That's a great question,and probably above my pay grade.
Stability will be a function of center of gravity,roll moment,yaw moment,pitching moment and center of pressure;and whether you want to design in oversteer, understeer,or neutral steering.
At low speeds,understeer is prefered,and you just give it more steering input.
At high speed you want to weather vane,and cancel out any induced yaw,otherwise the car will get away from you.
The GM Sunracer suffered understeer and they put a series if strakes along the underside of the tail to null out the nose's tendency to turn broadside to the wind rather than into it.
Since the template 'pumpkin seed' has won the World Solar Challenge a number of times,and had to remain stable in the presence of land trains on windy days,it acquits itself rather well under rough wind conditions.
Bucky's Dymaxion Car should have half the drag if it were a half-body (if you ignore the wheel drag).It would bring the CG down and that would frustrate roll.We know there was a fatal rollover incident associated with it,but that was the fault of a real rubbernecking nimrod who collided with it.I don't remember Bucky complaining about handling issues.
The Ford Probe-V is truncated,and with the vestigial fin on the boot,they claim excellent crosswind stability.