Aerodynamic Drag

Approach to the Problem

I'm a scientist and engineer. Math and engineering in electronics and mechanics, but no formal training in aerodynamics. I read some articles and books. See references below. Airflow around symmetrical smooth things like blimps is relatively straightforward. Airodynamics of classical airplanes is tractable, and is generally approached by treating fuselage flow and wing flow separately. Aerodynamics of bluff bodies are more complicated. A bluff body means something like a car or truck or bike, something that can't be wholely optimized for simple airflow drag characteristics. Understanding air flow around a bluff body requires a combination of theory and experiment. Experiment can include a component of simulation, along with a healthy dose of skepticism and requiring confirming experimentation.

Drag In General

For a bicycle traveling on level terrain, the majority of the cyclist’s physical exertion is expended to counteract the forces of aerodynamic drag. Aerodynamic drag may be categorized into skin friction drag and pressure (form) drag. A body with good aerodynamic drag properties should have a smooth exterior to minimize skin drag, and the amount of exposed surface area should be minimized. The shape should enable laminar flow on surfaces to the greatest extent possible, since laminar flow has lower drag than turbulent flow. More importantly the body should be shaped to avoid airflow separation. Separation leads to generation of vortex flows which transfer kinetic energy from the cyclist and bicycle into kinetic energy in the air, contained in trailing airflow vortexes. Transfer of energy means energy loss, thus drag force. Flow separation and the generation of vortices cause the majority of aerodynamic drag on a cyclist.

Airflow Around a Cyclist

For a cyclist riding on a bicycle, airflow impinging on the cyclist’s torso passes between and around the cyclist’s arms, toward the cyclist’s chest, then around the torso sides and over the back and buttocks. Airflow impinging on the cyclists head and face travels over and around the head, then over the cyclist’s back. Upon reaching the cyclist’s back and buttocks, flows from the head and flows passing around the sides of the cyclist’s torso separate and become detached, creating low-pressure regions. Flow circulation is generated in the low pressure regions, and that flow circulation bends into vortices which trail from the regions of the cyclists back and buttocks. Moving air in these trailing vortices represents energy expended by the cyclist and transferred to the air.

Airflow around the cyclist is affected by the relative position of the legs. When one leg is raised and the other extended, flow across the cyclist’s chest is crowded by the raised thigh and tends to flow preferentially across the chest toward the side with the extended thigh. Flows around the thighs detach from the back sides of the thighs, creating low pressure regions, flow circulation, and energy loss in trailing vortices.

Scale

Airflow is complicated. It doesn't simply scale with size. The airflow around a mosquito behaves differently from the airflow around a bird, which is different from the airflow around a rocket. Reynolds number is a dimensionless quantity used in fluid mechanics to characterize the tendencies of fluid flow. Mathematically it is the ratio of inertial forces to viscous forces. It is calculated as a function of velocity and dimension of a moving object, and dynamic and kinematic viscosity and density of the fluid. A Reynolds number of 500,000 represents the approximate boundary between laminar and turbulent flow. Flow at higher Reynolds numbers will be generally turbulent, and flow at lower Reynolds numbers will be generally laminar.

A bicyclist traveling at a velocity on the order of touring or racing speed has a Reynolds number of approximately 500,000. This means the flow characteristics lie on the boundary between laminar and turbulent. Flow over surfaces of the at the front of the cyclist's body may be laminar, then transitioning to turbulent toward the rear of the cyclist. Given this Reynolds number boundary region of operation, it may be possible to manipulate the flow characteristics toward laminar or turbulent in order to affect aerodynamic drag.

Strategies

Laminar flow attached to a surface has a lower drag characteristic than turbulent flow attached to a surface. As long as flow remains attached, lowest drag is achieved if the flow is laminar. But note that laminar flow is an ideal situation seldom achieved with an arbitrarily shaped aerodynamic body like a cyclist. It is generally more productive to concentrate first on large scale flows. Rather than optimizing for laminar flow around the front of the cyclist's helmet for instance, pay attention first to the trailing vortices from his buttocks.

For a body in an airstream, a typical first strategy for minimizing flow drag is to orient the body with its longer dimension in the direction of the airstream. This minimizes frontal area, defined as the shape of the object projected onto a plane perpendicular to the flow direction. Static pressure exerted by the airstream upon the body surface is a function of the flow velocity. Static pressure decreases with increasing flow velocity. Over the front portion of the object, as the body cross sectional area is increasing, the flow is accelerating, so the static pressure is decreasing. Under these circumstances flow typically remains attached to the surface of the body.

After the flow has passed the widest section of the body, the static pressure exerted by the fluid tends to decrease. When static pressure decreases with increased flow length along the body, this is referred to as a negative pressure gradient. Flow in a negative pressure gradient is more likely to separate from the surface, causing form (pressure) drag. To minimize drag, it is desirable to prevent flow separation. Or if flow separation cannot be prevented, it is desirable to delay flow separation to as far rearward as possible, and to minimize the amount of energy transferred to rotating flow vortices. In a negative pressure gradient turbulent flow may stay attached better than laminar flow. So given that a negative pressure gradient is inevitably occurring, it may be desirable to cause the flow to transition to turbulent, helping the flow remain attached. So we see that laminar flow is not always better than turbulent flow.

In summary, to minimize aerodynamic drag, a hierarchy of strategies can be stated as:

  1. Minimize frontal area.
  2. Avoid flow separation.
  3. If flow separation must occur, try to re-attach it and minimize the amount of energy transferred to rotational flow.
  4. Encourage turbulent flow to occur where this improves the pressure gradient and keeps the flow attached.
  5. Prefer laminar to turbulent flow. Maintain laminar flow over the front of bodies and as far rearward as possible.

References

The following do not include URLs, and are not fully formed citations, but you can easily find with a search. They vary from research papers in the public domain to published bound books.

General and Vehicle Aerodynamics

  • A history of car aerodynamics - G. Dimitriadis
  • Basics of vehicle aerodynamics Prof. Tam s Lajos
  • projects_for_the_amateur_scientist - bathtub aerodynamics
  • Fluid-Dynamic Drag, Hoerner 1965
  • FUNDAMENTALS_OF_AERODYNAMICS - John D. Anderson 1984
  • Methods for the drag reduction of bluff bodies and their application to heavy road vehicles
  • scaling laws in aerodynamics hydrodynamics - caltech
  • scientific american 1983-12-01: human powered land vehicles

Bicycle Aerodynamics

  • A Comparative Aerodynamic Study of Commercial Bicycle Wheels using CFD
  • A Phase-Averaged Analysis of the Pedalling Cyclist Wake
  • A quasi-static investigation of the effect of leg position on cyclist aerodynamic drag
  • Aerodynamic study of different cyclist positions CFD analysis and fullscale wind-tunnel tests
  • Aerodynamics and Cycling by jim martin
  • aerodynamics of cycling - Kulju.ppt
  • Aerodynamics of Time Trial versus Road Configurations - 2008 mark cote of specialized bicycle
  • airfoil development for the trek speed concept triathlon bicycle
  • An Aerodynamic Study of Bicycle Wheel Performance using CFD
  • Bicycle Design- A different approach to improving on the world hum
  • Cervelo P5-Technical-White-Paper
  • CFD simulations of the aerodynamic drag of two drafting cyclists
  • Consequences of Drafting on Human Locomotion - Benefits on Sports Performance
  • Cyclist drag in team pursuit influence of cyclist sequence stature and arm spacing
  • Defining, Measuring and Improving AERODYNAMIC TESTING IN THE BICYCLE INDUSTRY - Easton_Aero_WP1
  • Dominant flow structures in the wake of a cyclist - Crouch
  • Drag kings - characterizing large-scale flows in cycling aerodynamics
  • Flow interactions between two inline cyclists
  • Flow Separation Control with a Truncated Ellipse Airfoil in Cycling Aerodynamics
  • Flow Topology & Large-Scale Wake Structures Around Elite Cyclists - Crouch
  • Hart_Olympic-Sport-Paper
  • Human-Powered Vehicles - Aerodynamics of Cycling
  • Numerical study on the aerodynamic drag of drafting cyclist groups B.Blocken
  • On the Relevance of Aerodynamic Force Modelling Versus Wind Tunnel Testing
  • Recumbent Aerodynamics Blog Aerodynamics and Human Powered Vehicles
  • Surprises in cycling aerodynamcis
  • The aerodynamics of Human-powered Land Vehicles - Kyle et al in sci am 1983
  • The Effect of Spatial Position on the Aerodynamic Interactions between Cyclists
  • The Physics of Cycling MIT
  • The understanding and development of cycling aerodynamics
  • Validation of a mathematical model for road cycling

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