Aerodynamic Mirrors (fluid dynamics help?)

[edenstrang]

Okay, so after tuft testing the side of my metro, I confirmed with hard evidence something anyone could have told me, which is that the mirrors create a big ugly wake next to my window and sends my yarn spinning at least a foot back.

I want to install video cameras or inboard mirrors, but due to various motorcycle related circumstances I can NOT hazard being pulled over! Like, jail, dig it? But let's not make that the topic of this thread...

Basically I need something reflective that sticks out of the side of my car, and preferably does double duty as a means of seeing behind me. I was just re-reading Gravity's Rainbow, and got inspiration from the V-2 rocket. This is my idea-



The gray semi-circle at the right end represents a 2" convex mirror. The gray triangle in the background is the mount on the car.

Is there any rule of thumb, independent of scale or viscosity, for the optimal proportion between the width, length, degree of taper, widest point, etc? Do I have a way of knowing whether my truncated 'Kamm' section will be narrow enough, or set far enough back, without testing? I tried looking through Horton's book, but briefly, and I didn't find any reference.

Also- I instinctively made the tip pointed, from whatever naively ingrained notion of what an aerodynamic shape is, then realized that I never see a solar car/HPV/modern projectile with a pointed tip. What's the lowdown? If you were to make a tip that was entirely spherical, that would have the same frontal area, no? Just at a more severe angle of attack...

So many questions!

[brucepick]

A pointed tip catches the "wind" as it moves forward. Also, if there's any crosswind at all you end up with the airflow coming in at an angle instead of head on.

A blunt tip (I think a parabolic curve is usually used, or something close to parabolic) lets the airflow find it's own path of least resistance. Also used on torpedoes and many boats.

However at the trailing edge, a taper to a thin tip or edge is a good thing. It encourages the airflow to rejoin itself smoothly. An airplane wing is a good example of both the rounded blunt leading edge and a tapered trailing edge.

[edenstrang]

Originally Posted by brucepick

A pointed tip catches the "wind" as it moves forward. Also, if there's any crosswind at all you end up with the airflow coming in at an angle instead of head on.

A blunt tip (I think a parabolic curve is usually used, or something close to parabolic) lets the airflow find it's own path of least resistance. Also used on torpedoes and many boats.

However at the trailing edge, a taper to a thin tip or edge is a good thing. It encourages the airflow to rejoin itself smoothly. An airplane wing is a good example of both the rounded blunt leading edge and a tapered trailing edge.

Thank you! That solidifies several unformed biases floating around in my head against the pointy tip.

My only design limitation is that the rear must be a 2" convex mirror. I've considered shrouding it with a transparent plastic cone, but I don't want to optically handicap what's already a tiny rear-view. If I can 'virtually' shroud it with Kamm's cut-off, that would be ideal...

[lunarhighway]

before you get all exited about designing a super smooth shaped mirror (wich is fine of course), take into account that the drag caused by any object is the combination of drag quoefficient and frontal area!... and since you have not only the mirror but also the mount to take into account, perhaps motorcycle style mirrors are somethign to considder... most passenger cars use mirrors on big mounts to allow for mechanisms to adjust them from the inside, but if you can live without that you could mount the same mirror surface on a much smaller and thinner support that will allow the air to stay attached to the side of the car. some sportscars also use thin wide mirrors... so maybe you could reduce the height of the mirror to save frontal area as well without loosing to much usefull information from behind you.

[Mighty Mira]

"If I can 'virtually' shroud it with Kamm's cut-off, that would be ideal..."

I really should edit that wikipedia article that seems to be responsible for perpetuating the bs that a Kamm back can create some sort of virtual and equivalent teardrop shape. It can't. It's an engineering trade-off. You cut it sharply at the point of diminishing returns. Most of the drag of a truncated teardrop will be in proportion to the cross sectional area of the truncation.

At some point, the decreasing area becomes not worth worrying about in relation to practicality concerns, or cost, or that there are enough other big drag causes (e.g. wheels) that aren't addressed, that it is myopic just to focus on extending the teardrop.

Even the jumbo jet has a "Kamm back", i.e. a point at which the extra reduction in drag coefficient are not worth the extra weight or decreased thrust by having a longer exhaust for the auxiliary engine.

But there is nothing magical about it that enables it to cure the low pressure region at the back of the Kamm back.

Another way of looking at it if the taper is in two dimensions, with the beginning area of the taper starting at W0, length from that beginning as L, with taper angle "theta", the cross sectional area = (W0)^2 -2(W0)(L)Sin(theta) + (L^2)(Sin(theta))^2

Most of the gains occur close to the beginning, with not much to be gained by extending the taper to a point. Tapering in at the sides will have negative consequences in crosswinds more of the time than a car without such taper, since the crosswind will only need to be slight in order for the boundary layer on the surface on the lee side of the crosswind to become detached, and hence, low pressure with a component of the resulting force towards the rear of the vehicle, pulling you back.

Note that if the taper is only in one direction, the reduction in area will stay linear, meaning you might as well taper to an edge if you can.

[caveatipse]

You could make the mirror itself a teardrop shape with a pointed tail, and mount it directly to the car so that there is no need for a mount.

[SL8Brick]

Originally Posted by edenstrang

I was just re-reading Gravity's Rainbow, and got inspiration from the V-2 rocket.

Also- I instinctively made the tip pointed, from whatever naively ingrained notion of what an aerodynamic shape is, then realized that I never see a solar car/HPV/modern projectile with a pointed tip. What's the lowdown? If you were to make a tip that was entirely spherical, that would have the same frontal area, no? Just at a more severe angle of attack...

The V2 rocket, including many other rockets, missles, jet-powered aircraft use the pointed tip to help traverse the speed of sound. High powered rocketry used to be a hobby of mine and we followed the same guide lines. High impulse rockets intended to break the sound barrier always used pointed nose cones while low impulse/long thrust duration high altitude models used parabolic nose cones. I think the point in the nose allows for more efficient air compression in the trans-sonic phase.

[edenstrang]

Originally Posted by lunarhighway

but if you can live without that you could mount the same mirror surface on a much smaller and thinner support that will allow the air to stay attached to the side of the car.

I asked for this, by not being more explicit with my diagram.



This is the front of the mirror, it is it's own body. I'm sure the fairing between the mirror/foil/car won't be optimal to reduce clashing boundry layer drag, but if the improvements are even measurable I'll be esctatic. EDIT: I'll probably be ecstatic, too

Originally Posted by Mighty Mira

But there is nothing magical about it

I had a sassy retort for this one, until I realized that the rest of the post answered my questions exactly. I chose poor phrasing too, I'll admit immediately, and will watch my step from here on. I was trying to imply that I thought the taper (not the mystical void beyond, granted) on the body would aid a reduction in drag given the logistical compromise necessary to fit a flat mirror on the end, a hundred lame apologies.

Originally Posted by theclencher

zx2 posted a pic of a clear boattail for his mirrors once... if anyone would just look for it. there are threads with mirror deletes, mirror delete tests, and interior mirrors too. it's true!

I did a search, but only one thread came up critiquing my proposed mirror shape. It was this one, so I regret nothing

[Mighty Mira]

I'm not sure why it is instinctive that we tend to shy away from smooth, blunt shapes that approach the point of largest cross sectional area parallel to the expected direction of travel. These have the least drag associated with them in the subsonic regime.

I suspect that it's either looking at fighter aircraft and rockets designed for transonic/supersonic regimes, or that we are used to sharp points/edges with things like darts, axes, knives etc for piercing solids where the solid has fairly high forces of cohesion. Almost all of the work done in cutting something like a rope is done in severing whatever is holding a tiny area of the material together, pushing the remainder of it out of the way once cut is minimal by comparison. So for that you need a point or an edge to induce that force in a small area.

We've had edges and points for so long that our understanding of them would have to be ingrained in our genetic code by now - those who had an instinctive understanding of edges/points would have had an edge since hunter gatherer days.

Boats we have had a long time, although the difference between a blunt end and a sharp end is mainly a refinement. A dull edge will not cut, but a boat with a pointy hull will still sail.

This document on rocket nosecones is interesting.

Below Mach .8, the nose pressure drag is essentially zero for all shapes. The major significant factor is friction drag, which is largely dependent upon the wetted area, the surface smoothness of that area, and the presence of any discontinuities in the shape. In strictly subsonic model rockets, a short, blunt, smooth elliptical shape is usually best.

For our application, it seems as though short, blunt, elliptical type fronts would be best for the front end of a mirror. For areas close to the ground (e.g. front end of a vehicle) you want the air to be flowing up and over the car, so at the very least it should be perpendicular to the front of the car and perhaps/probably raked back somewhat.

The alternative is to raise the body of the vehicle above the ground somewhat to reduce ground effect, but there are other issues associated with that (more torque from crosswinds, marginally more side area, need wider wheelbase for stability in cornering). The best road vehicle drag coefficient in the world is the Pac-car, with a Cd of 0.075, and utilizes this concept.

[edenstrang]

Cool, I'm confident in my revised design now... I'll post a drawing.

The mirror will be a one-off fiberglass-over-foam affair, with all the sanding and body filler that goes with that. In theory I could make a mold and pump out a few more for fellow metro-types that have inspired me. Skewbe? MetroMPG?