As already mentioned, the mechanical models commonly used in the engineering community are inadequate to fully account for the drag forces on vehicles having wheels fully-exposed to headwinds. Mechanical models used in the design of aerodynamic wheeled vehicles should account for both the effect of augmented drag forces on the upper wheel surfaces — which significantly retard vehicle motion — together with the enhanced traction that results from shielding these upper wheel surfaces.
Designing aerodynamic wheels using a faulty mechanical model for overall vehicle drag, for example, can lead to sub-optimal products. Deep rims found on many racing bicycles suffer from the extended surface areas of these aerodynamic rims. The extended surfaces are exposed to headwinds at the worst position for minimizing vehicle drag, near the top of the wheel. Thus, the intended reduction in vehicle drag by using these aerodynamic rims is largely offset by increased frictional drag on these surfaces. Perhaps this is one reason there has been no convergence on a single rim depth as the clear winner in terms of overall drag reduction.
As mentioned, the bicycle industry tends to inaccurately test road bikes in wind tunnels. Wind tunnel testing has been developed by the aerospace industry over the years primarily to test flight vehicles. Hence, the pedestal instrumentation used to measure drag forces in wind tunnels has been designed specifically for the testing of airplane models. Engineers simply adapted this existing instrumentation for use on bicycles. However, the drag mechanics for wheeled vehicles is considerably more complicated than for non-wheeled vehicles. This condition has not yet been properly recognized, and is a subject of the pending patent application.
- Wind-Speeds Far Exceed Vehicle Speed on Upper Wheel Surfaces
- Wind-Speeds Approach Null on Lower Wheel Surfaces
- Wheel Drag Highly Concentrated on Upper Wheel Surfaces
- Headwinds Exacerbate Vehicle Drag on Upper Wheel Surfaces
- Power Dissipation in Drag is Proportional to Cube of Wind-Speed
- Faired Upper Wheels Substantially Reduce Vehicle Drag
- Faired Wheel Gains Rapidly Increase in Stronger Headwinds
In part, the proper vehicle wheel drag model may be simply understood in relation to the wind profile across the wheel. The effective wind speed for surfaces located at the top of the wheel is twice the vehicle speed, while the wind speed for surfaces at the bottom of the wheel is null, as the wheel is contact with the ground. Since drag force arises in proportion to the square of the effective wind-speed, it becomes apparent that the upper wheel surfaces are quite sensitive to drag forces, while the lower wheel surfaces are much less sensitive. And it should be noted that other factors augment this relationship.
These upper wheel drag forces are particularly critical in retarding vehicle motion, due largely to the faster wind-speeds present on exposed surfaces, and to the relation between wind-speed and the power required to overcome these drag forces. The power required to generate the needed propulsive counter-force rises in proportion to the cube of the effective wind-speed on drag-inducing surfaces. Hence, the additional propulsive power needed to overcome rising headwinds increases quite rapidly. This is an important factor contributing to the dramatic slowing cyclists face when riding against a headwind. Upper Wheel Fairings nullify most of this critical wheel drag — thereby optimizing a bicycles' potential performance — allowing cyclists to better penetrate against headwinds.
The drag model indicates that speed gains increase quite rapidly in only modest headwinds. Under null headwind conditions, the predicted gains are minimal, which is consistent with road test results. However, whenever a headwind is present, the gains rise rapidly, with the increasing gains tapering somewhat in very strong headwinds. This is apparent from the relative speed gains chart, which shows predicted gains in speed of a typical road bike versus external headwinds.
- Gains Quickly Increase When Facing Even Light Headwinds
- Gains Continue to Increase When Facing Stronger Headwinds
- Gains Depend on Ratio of Wheel Drag to Vehicle Drag
- Greater Gains for Smaller Riders on Non-Aero Bikes (Upper Curves for High Spoke Count Wheels)
- Road Testing Confirms Predicted Gains Trends from Drag Model
The relative speed gains chart shows a series of data curves, with each curve representing a road bike configured with a different ratio of wheel-drag to total vehicle-drag. Bicycles with low-spoke count aerodynamic wheels or with larger riders will have relatively more drag on the vehicle frame and rider, than on the wheels. Hence the power saved by shielding the upper wheels will represent less of the total vehicle drag, than that with bicycles having non-aero wheels or smaller riders. Thus, the lower curves showing less gains represent the fastest race bikes, while the upper curves showing more gains represent more standard commuter road bike configurations. Still, the gains shown for either style bicycle are significant.
The relative speed gains chart can be represented differently in absolute terms — rather than relative terms — by assuming a bicycle traveling at 10 mph, for example, facing headwinds up to 40 mph. This absolute gains chart shows the predicted gains in mph against a headwind. For example, a bicycle having a wheel drag ratio of 15 %, and traveling at 10 mph into a 15 mph headwind, would achieve a theoretical gain in ground speed of 1.0 mph. This represents a 10 percent relative gain in vehicle ground speed. This gain is typical for a very common headwind condition for most riders.
As mentioned, industry typically designs bicycle aerodynamics in wind tunnels. Designing to wind tunnel test results tends to compare bicycles in an effective null headwind road condition, where headwind effects are minimized. From the gains chart it becomes apparent why industry may have overlooked the benefits of wheel fairings. Under null headwind conditions, vehicle gains in speed are minimal with upper wheel fairings. The extra surface area of the fairings may even offset the minimal predicted gains in most configurations.
It is only when facing an external headwind under real-world road conditions that gains in vehicle speed are readily achieved by using upper wheel fairings. In the past, wheel fairings have been tested in wind tunnels with wheels not touching the ground. This test configuration does not mimic a real-world road test. And testing bicycles on test fixtures with instrumentation attached to the pedestal in the same way used to test aircraft models, also does not mimic real world road conditions.
Further Characteristics of Wheeled Vehicle Drag Mechanics
""...And what's reduced is that 'fist in the chest' feeling with a direct headwind gust. I still do feel a direct gust on my chest if I'm not on the tops, but the accompanying brake-slam on the bike doesn't happen."
—Lou Normadeau, Long Distance Touring Cyclist
- Upper Wheel Drag Component of Total Vehicle Drag Quickly Increases When facing even a Light Headwind
- Cubic Relation of Power Dissipation Causes Faster Upper Wheel Surfaces to Rapidly Induce More Drag with Minor Increases in Headwind Speed
- Upper Wheel Drag Forces are Mechanically-Advantaged Over the Propulsive Counterforces Applied at the Axle
- Both the Augmented Headwind Sensitivity and the Mechanical Advantage Both Combine to Exacerbate the Vehicle Drag-Inducing Sensitivity of the Upper Wheel Surfaces
- Extreme Upper Wheel Drag Sensitivity Responsible for Dramatic Slowing of Bicycles When Facing External Headwinds
- Gusting Headwinds Repeatedly Slow a Cyclist, Exacerbating Rider Fatigue from Cyclic Braking and Re-Accelerations
- Faired Upper Wheels Nullify Most Wheel Drag Headwind Braking Cycles, Reducing Rider Fatigue
- Shielding Faster-Moving Upper Spoke Surfaces Shifts Drag from Upper Wheels to Slower-Moving Streamlined Vehicle Frame Surfaces
- Slower-Moving, Low Drag-Inducing, Lower Wheel Surfaces Should Remain Exposed, Unshielded by Faster-Moving Frame Surfaces
- Upper Wheel Fairings Nullify Wheel Drag Sensitivity to Headwinds, Maintain Headwind Penetration Speeds, Enhance Rider Safety and Reduce Rider Fatigue