• Vis
• Rediger
• Historie
• Udskriv

CoastDownTest

Coast Down Test

- A Method for Determining Aerodynamic Drag

Author: Mark Olaf Slot, Cand. Polyt.
August, 2001. Revised July, 2003

Have you ever wondered exactly how big (or small) the aerodynamic drag of your (recumbent) bike is? It is commonly known that recumbents are faster than ordinary bicycles. By now, it is also commonly known that the reason for this is that recumbents have less aerodynamic drag. But how much faster are they? And how much less is the aerodynamic drag? What about front and tail fairings, disc wheels, aero helmets etc.? Do they have an effect, or are they purely psychological? These questions are often answered with some vague feelings, instead of presenting proven figures.

The most obvious thing to do is of course to test all the bikes and equipment in a wind tunnel. We have several suitable wind tunnels here in Denmark. However, the price is too high for the average recumbent enthusiast. The price is about € 5.000 per day, everything included. That is why I have been looking for a cheap and simple method for determining the aerodynamic drag.

Many cyclists surely have coasted down a hill side by side with a friend, just to find out who is rolling faster. Surely, this has something to do with the aerodynamic drag. But weight also has some influence, so this gives no equivocal proof as to who has less aerodynamic drag. Heavy riders just roll faster, but are not necessarily faster uphill (this is the law of gravity!).

The aerodynamic drag can be calculated with this equation:

Where r is the air density, v is the relative velocity of the bike to the airflow, CD is the aerodynamic drag coefficient and A is the frontal area. In this connection, the interesting thing is the aerodynamic drag index, which is the product of the aerodynamic drag coefficient and the frontal area (CD·A).

Simulation Program

By writing a computer program, a coast down test can be simulated, taking all relevant factors into account. I have written a program like this, which performs a time simulation, based on the physical equations of motion of the bike. That means that forces, velocities etc. are calculated stepwise as the bike is coasting down the hill. If the program is fed with all relevant data (slope course of the hill, meteorological conditions, mass of bike + rider, rolling resistance coefficient and aerodynamic drag index), it is able to calculate the course of the velocity all the way down the hill as well as the top speed.

• The course of the hill slope can be read from the contours on a detailed topographic map.
• The meteorological conditions can be measured with standard measuring instruments.
• The mass of bike + rider can be measured with a scale.
• The rolling resistance coefficient can be looked up in a table, if the tire brand, size and inflated pressure is known.
• The aerodynamic drag index is the unknown quantity, and in principle one has to guess the value of the aerodynamic drag index, until the program calculates exactly that top speed, which was achieved in the real coast down test. The process of guessing can of course be automated; thus in this program a smart routine automatically refines the guess, and finally writes out the result.

The program takes into account many details, which would be impossible to calculate by hand. Among other things, this includes influence from the rotating mass of the wheels, influence on the rolling resistance from bumps in the road surface, air pressure, temperature, possibly a head or tail wind component etc.

The “Vissenbjerg Hill”

Height profile of the “Vissenbjerg Hill”.

I have been searching the region for some good hills, which could be suitable for performing coast down tests. The hill should be sufficiently long and steep, so one can attain a good speed, and it should preferably be sheltered, so the wind has minimal influence on the measured results. In addition, there should be no sharp curves or crossroads, which could be hazardous, when racing down at high speed.

In the end I decided on a road called Kirkehelle in the village Vissenbjerg in south-bound direction towards Skalbjerg and Tommerup St., generally just called “Vissenbjergbakken” (“Vissenbjerg Hill”). The hill is about 1.1 km long and has a total drop of about 60 m. The average slope is 5.5%, but the upper half of the hill slopes about 7% on average, and in some places up to 12.7%. The Technical Administration at the local authority in Vissenbjerg provided me with a very detailed topographic map (scale 1:1000) with 0.5 m contours. I have read the height/slope course from this map. The hill has no hazardous crossroads, and just some very flat curves, where it is possible to go full speed without any problems. A forest shelters the upper half of the hill.

The beginning of the hill (indicated with length 0 m) is defined as the middle of the traffic light crossroad at the top of the hill.

The picture to the left is taken about 60 m from the top of the hill, and shows the sheltering forest at the upper half of the hill. The picture to the right is taken about 350 m from the top of the hill, and shows the flat bends just before the flat part on the middle of the hill.

Calculation Examples

Here is a calculation example of the speed course for a typical recumbent bike. The top speed (in this example 64.5 km/h) is normally attained at about the middle of the hill, just before the flat part. Therefore, in practice it is enough to coast down to the flat part on the middle of the hill to record the max. speed on the bicycle computer.

Calculation example for the speed course for a typical recumbent bike.

In the figure below it is shown how the forces on the bike vary on the way down the hill.

Calculation example for the aerodynamic drag, rolling resistance drag and the gravity component for a typical recumbent bike.

In the figure below it is shown how the top speed typically depends on the aerodynamic drag. This is only one typical example, as the top speed also depends on the mass of bike + rider, the rolling resistance, the wind etc.

A typical example showing how the top speed depends on the aerodynamic drag index.

Uncertainties

How accurate is it to determine the aerodynamic drag index by such a coast down method? Some practical tests show that the program calculates a speed course, which is very close to the real speed course in the coast down test on the “Vissenbjerg Hill”. The accuracy of the results depends primarily on the uncertainties for the input data for the program (e.g. the accuracy of the mass of bike + rider, the rolling resistance coefficient etc.). The table below shows how much the uncertainties of the input parameters affect the results for a typical recumbent bike.

The uncertainties of the input parameters give cause for deviations in the calculation results.

*) The sensitivity for uncertainty of the initial speed is negligible in case of a standing start. However, tests have shown that the sensitivity is very large in case of a flying start, and should therefore be avoided.

The combined uncertainty for the aerodynamic drag index, where every single uncertainty is taken into account, in this case yields 14.5%. From this, the wind speed is by far the largest uncertainty, but also a possible speedometer measurement error matters a great deal. The speedometer measurement error is easy to avoid by calibrating the bicycle computer, i.e. to key in the exact wheel circumference (with fully inflated tires and loaded bike). By repeating the coast down test e.g. 10 times, and taking the average of the attained top speeds, also the influence from the wind can be reduced, and the statistical uncertainty from the wind speed is reduced to 4.3%. Therefore it is still important that the wind is not too strong or gusty, as this is the primary source of uncertainty.

How Do I Perform My Own Coast Down Tests?

First you need a good hill. The hill should probably have a total drop of min. 20 m, an average slope of min. 5% and have a length of min. 400 m. The bigger hill the better. This ensures a sufficient high speed and enough time at high speed for the aerodynamic drag to make any discrimination of different bikes. Look for a hill with a smooth road surface and no hazardous traffic, crossroads or hairpin bends! A sheltered place (e.g. in a forest) is desirable.

You also need a detailed topographic map of the hill, so you can make an exact height profile of the hill. 1 m contours are desirable.

Furthermore you need a bicycle computer, which can record the max. speed. Notice that some computers have an accuracy of the max. speed of 0.5 km/h. However 0.1 km/h is preferable.

Of course you need a scale to weigh your bike and yourself, and a thermometer and a barometer to measure the meteorological conditions. A wind speed measuring device would be very nice to have. However, most cup anemometers don’t rotate at all at low wind speeds due to bearing friction, so they are not very suitable for this purpose. However guessing the wind speed is better than nothing.

And last but not least, you need a person with a scientific background to arrange the coast down tests and make the calculations. If you are such a person, I can give you a free copy of the program, which runs on a standard PC. You can contact me by e-mail (mark -at- liggetandem -dot- dk) or by phone (+45 65 93 45 44).

You can find results of one such test in 2003? on this site.

IsEnglish