# What is the drag / power lost to a safety flag?

I have a recumbent bike that has a safety flag on the top of a thin pole, so it flutters around higher than and after my head.

How much power am I losing to this flag that could be used to power my ride forward?

How can it be measured as a wattage ? Sadly I don't have access to a power meter or a wind tunnel.

• arc.aiaa.org/doi/pdf/10.2514/1.9754 refers to aerodynamic drag of streamers and flags, but its not particularly helpful on the matter of power needed, and focuses on fluttering and oscillations and aspect ratios.
– Criggie
Feb 6, 2019 at 3:57
• My first though is a few orders of magnitude less than the power lost by a collision with a car. :) Feb 7, 2019 at 7:36
• @mattnz fair point - I'm going to try Mr Chung's suggestions, with no flag, the flat flag, and my flappy side-to-side flag. I'm sure they will have some cost, but is it negligible or is it significant? Going to put a gopro so it sees the bike computer, and I'm going to use strava's speed numbers as a second sensor. More news to come, but will take a couple weeks.
– Criggie
Feb 7, 2019 at 8:02
• My bet is that you'll be surprised at the amount of drag. I can easily spot the difference in CdA between wearing a tight and a loose jersey. (That said, using a flag may be worth it to you). I've measured the CdA and Crr of some unfaired recumbents; I was surprised. Good luck with your measurements. Feb 7, 2019 at 14:37
• I (mostly) said that in jest :). Please do report back your findings, should be interesting. Feb 7, 2019 at 20:10

If the pole is a flexible one, you can do the following:

• Choose a windless day

• Ride past a second person at a known speed

• Let the second person take a picture while you pass

• Repeat immediately in the opposite direction to capture the effect of the remaining wind.

• With the bike still, pull the flag back, measuring the force somehow. You can use a spring scale, or just hang a bottle with different amounts of water on a string, connect that string to the pole, and run the string over pulley or a round, smooth piece of metal.

• Take more pictures of how you are pulling the flag back.

• Compare the pictures of the bend pole while riding with the pictures while pulling the flag back.

With this method, you get the force that the flag exerts on you while riding the given speed. Now simply multiply with your speed, and you get the power that's drained by the flag.

Note: Work with the correct units. `1kg` weights `9.81N`, and if you multiply the force in `N` with your speed in `m/s`, you get `Nm/s = J/s = W`. Just make sure that you convert the inputs to the multiplication correctly.

• Minor pedantry: this only accounts for the flag's drag, not that of the pole itself (at least not fully). But it's still a clever answer :) Feb 6, 2019 at 16:31

Your question is similar to this bicycles.SE question.

Estimating aerodynamic drag can be tricky, but can be done with field tests. If you can find a quiet road that is protected from the wind and you have a way to record speed each second, you can do coast down runs to determine the drag with and without the flag. The approach is discussed on page 108 here. You do need a recording device to capture speed each second, but nowadays many riders use bike computers with this feature. If you have a device such as this and a speed sensor on your bike, you need no other special equipment.

Details are provided in the link but, in summary, you will want to do at least two runs starting at different speeds, then solve for the two unknowns of CdA (drag area) and Crr (coefficient of rolling resistance) given that the road surface and road profile are the same for both runs. Since your Crr should remain constant across runs, that will give you another constraint to use to evaluate the estimated CdAs.

The advantage of this method is that you can see when the run is spoiled and should be rejected. That is, you can spot a change in wind, or a passing car, or a change in other conditions. The sample size is the length of the run in seconds, not the number of total runs. You do want to have a wide variation in "entering" speeds so the runs are statistically independent and you can "pry apart" the estimates of CdA and Crr.

This method is a special case of the Virtual Elevation method where one uses an accurate power meter to collect the data. In this special case, we know that power while coasting is zero, so accuracy in power is not an issue. However, as in all estimates using Virtual Elevation, you will want your speed measurements to be as accurate as possible, so it's best to use a separate wheel sensor and to measure wheel roll-out accurately. Measurements of CdA attained using Virtual Elevation have been validated with wind tunnel measurements, and VE is the basis for most of the field tests done by pro cycling and Olympic teams. They use power meters not because the method requires it (the mathematics is exactly the same) but rather because data collection is faster: you can go both uphill and down, and it's easier to get a broad range of speeds since you can pedal. In typical coast downs, you are limited in the range of speeds you can easily attain and the length of uphill segments is short.

Once you have CdA and Crr, you can estimate the power "cost" in terms of watts from your flag at different wind speeds, not just at a given speed. The conversion formula for converting to power is given in one of the answers to that previous bike.SE question.

• While this is certainly true (+1) I suspect the effect is similar to the error margin, especially as even a light wind is variable (I know you acknowledge the need for repeats in that pdf but it's quite a significant point). You'd probably want to do a couple of runs with the flag, a few without, a couple with until you've got about the same number of each interleaved to take out slow changes in wind speed/direction and air density (which can change rather fast e.g. on a sunny morning as dew evaporates and the temperature rises) Feb 6, 2019 at 9:29
• Generally, there are two sources of error: random and systematic. In field testing, with this method, the random component of error is low; the systematic component can be high -- but the virtue of this method is that it provides not just an estimate but also a diagnostic of the error. That's what the virtual elevation profile is -- it's the diagnostic. You can spot when the wind is variable, or when rho changes. In early velodrome testing of the method, we spotted a change in air density when a door was opened and outside air was let in. Feb 6, 2019 at 15:24
• Interesting. I assumed variations in wind would show up as random errors, and I'm wary of any factor that's prone to steady drift over the course of an experiment. I assume you need a very good elevation profile to compare against - so accurate mapping data or a barometer rather than raw GPS Feb 6, 2019 at 16:38
• The one thing you can be pretty sure of is that there won't be much drift in the road gradient during your runs, so that's the main constraint you want to exploit. The true elevation profile is key if you want to identify Crr (since Crr scales like road gradient) but you can identify relative changes in CdA even if you only have an estimate of the true road profile. Fortunately, in my area the sewers are gravity-fed so I was able to get a handful of the heights of the rims of sewer access covers to sub-centimeter accuracy from the public works department. Feb 6, 2019 at 17:10

I think the trick will be to measure (ideally log) the force and multiply by the ground speed on a still day. An answer to an old question of mine has some useful formulae for reference.

The force is proportional to the square of the wind speed (or simply the speed as I've suggested a still day) so it would be better to multiply the instantaneous values and not just work with averages.

Now how to measure the force?

If we assume only the flag contributes to the drag, and not the pole, then connecting the flag to the pole with a strain gauge would work.

If we want to take into account the drag of the pole, then I suggest attaching the bottom of the pole to a pivot with a guide so that it tries to tip backwards, then using a strain gauge to prevent it doing so, mounted above the pivot. In this case you could actually use a spring balance instead of a strain gauge, remembering that they measure mass not weight (in physics terminology). At this point the leverage comes into play as well. Wikipedia has the leverage equations and some background, and you need to treat the pole and flag as separate sources of torque. You can probably just about treat the drag on the pole as a force at the centre of the bit exposed to the wind, and the drag of the flag as acting at the top. You could measure the force on the pole without the flag, and then the force from both, subtracting the first to work out the torque due to the flag.

If you can't log a strain gauge electronically, or you use a spring balance, you can always video the display with a clock synced to your speedometer.

• To be continued. This was going to be a comment originally but grew. I'd like to run the numbers working backwards from a guess to get an idea of the forces involved, but I'm not doing that on my phone Feb 6, 2019 at 7:21