# How to Calculate Drag Load of Sticker on Fast Moving Vehicle

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1. Feb 18, 2017

### enotyphoon

Hi Great Engineers,

Need you help. I am required to calculate drag load on sticker to ensure it is not peeling off in operation. The vehicle may moves as fast as 220 km/hr with rectangular sticker size of 30 cm x 40 cm, thickness 0.0635 mm on its body. Wind direction is parallel to 40 cm length and perpendicular to 30 cm sticker length.

My first though is using (1/2)*row*A*V^2*Cd basic formula to get the drag load.
for each value :

A = 30 cm * 0.0635 mm ... (unit conversion will be done in actual calc.)
V^2 = 200^2 km/hr .... (unit conversion will be done in actual calc.)
Row = density of the air at that altitude
Cd = not sure about the valid strong value for reference, but i will use the Cd for rectangular shape which have been establish in few reference to NASA docs. May change if I found another publication that I feel confidence.

Does this method acceptable?

Is there is another factor that I need to take into consideration? Please do highlight.

My purpose is not to get accurate answer on the drag load, but being conservative is good already. Our main objective is just to ensure it wont peeled of during operation. So accurate value of drag load is not necessary.
If required to install any test set to gain some value on vehicle is also impossible as we have no access to it and may cost money for operation.

the sticker that i used is ORACLE 651 material. Datasheet can be found on the net.

Last edited: Feb 19, 2017
2. Feb 19, 2017

### Baluncore

As the leading edge of the sticker starts to curl and lift, the rectangular edge will increase in height above the surface so the area and force will increase. When folded back 180° the thickness will be more than double.

Air will then enter the space between the sticker and the surface. That will tend to lift the sticker.
What will that dynamic air pressure be?
Should you allow for rain drops or puddle splash which will have a much higher density than air?
Pa = 0.5 * density * v2. Density of air = 1.225 kg/m3. Density of H2O = 1000 kg/m3

Any bubble that forms under the sticker will concentrate the lifting force to the remaining glue along the circumference of the bubble. Is the glue strong enough to hold?

Oracle Adhesive power* (FINAT TM 1, after 24h, stainless steel) = 18 N/25 mm

3. Feb 19, 2017

### Staff: Mentor

Can you just paint it on instead?

4. Feb 19, 2017

### Baluncore

This would be a really interesting problem to solve. Please don't spoil the insight acquisition = fun.
Velocity = 220 km/hr = 61.111 m/sec.
Air; Pressure = 2.287 kPa.
H2O; Pressure = 1.867 MPa.

5. Feb 19, 2017

I'd be very surprised if the pressure drag described by the proposed drag formula was the dominant factor here. I think viscous shear stresses will be a larger factor locally, as they will act over the entire length of the sticker and in a direction that would tend to peel the sticker off. At the very least they will be important.

Unfortunately, those would also be more difficult to actually calculate. You would need some means of estimating the shape of the boundary layer so that you could estimate the velocity gradient at the surface.

6. Feb 19, 2017

### Baluncore

“Viscous shear stresses” will cover the surface area, but the same area of glue will counter that shear. The critical failure mode will be at the leading edge of the sticker where it lifts and folds backwards. Peel will begin at the leading step, well before surface shear starts to drag the sticker across the surface. The glue is the same for each effect.

Protection of the leading edge could make a big difference. That protection could be a glue fillet or taper to the leading edge of the label. It might also be possible to roughen the surface ahead of the sticker, so as to separate the laminar flow before it reaches the sticker.

7. Feb 19, 2017

I am not sure why you are placing that in quotes, because it isn't exactly an imaginary concept. Anyway, I never said the sticker would be dragged across the surface, nor did I imply it. In fact, if we really want to be picky, purely based on forces, the drag due to air impacting that tiny front edge is going to produce a force that only serves to "push" the sticker along the surface unless there is already a portion of it that is peeled slightly, so your above point applies equally well to the air impacting the front.

Now, here is where my suggestion comes into play. There are two parts to this, both due to the formation of a boundary layer where the velocity of the air at the surface is zero:
1. The sticker is thin. Even if the air is traveling at 200 kph past the surface, that velocity will go to zero (relative to the surface) as you get closer and closer. This sticker is 63.5 microns thick. Relative to the car, the air is probably moving at least one order of magnitude slower than that at that height off the surface. We are talking single digit meters per second. That is going to produce a tiny amount of drag purely from pressure differentials.
2. Viscous shear, which will be quite large, is going to be counteracted by the glue. However, while that is true, it will form a couple and the resulting moment on the sticker will be in a direction such that this is actually the mechanism that will tend to cause the sticker to start to peel up. This would be independent of whether you added a fairing to the front of the sticker unless that fairing's purpose was to increase adhesive strength at that leading edge.
First, roughening a surface does not promote flow separation, and if the incoming flow is laminar, it is more likely to actually delay separation. This is how a golf ball works. The roughness will likely cause rapid onset of turbulence, which makes a boundary-layer less susceptible to separation.

Second, there's no guarantee that the boundary layer will even be laminar where this sticker is placed. Whether the boundary layer on a car is laminar or turbulent will obviously depend on the car's shape and where on the car the sticker is placed. Suffice it to say, though, that there is a sizable extent of turbulent flow over a car.

Finally, if you did manage to separate the flow before the sticker, you are going to dramatically increase overall drag on the vehicle, which is probably not very desirable.

8. Feb 20, 2017

### jack action

This problem is impossible to solve with such simplicity. Where the sticker is placed on the car plays a major role. For example, if the sticker is put on the top of the hood of a typical saloon car or on the top of its trunk, the flows are completely different at these locations.

It's probably a lot simpler to test than try to evaluate theoretically.

On the top of my head, to be on the safe side, a glue that can resist a pressure differential of 1 atm (the highest vacuum possible that can be created over the sticker) seems to be a good starting point.

9. Feb 20, 2017

Certainly, but at least getting the qualitative picture correct will help narrow down what physics are most important. The problem is qualitatively not intractable. Quantitatively, it's essentially unsolvable analytically. It would need only rough, order-of-magnitude type calculations by hand, or else a numerical model or an experiment.

True, though the same fundamental principles apply regardless of its location, i.e. pressure and viscous forces are really the only two that may play a role. No matter where it is placed, there will be a boundary layer, and that will feature zero relative velocity at the wall. If you placed the sticker so that its front edge was very near the stagnation point, that's the only situation I envision that might result in the pressure along the leading edge being important, and even then it will be in addition to the viscous stress.

You can certainly experience greater than 1 atm of pressure differential. Sure, you can't go below 0 absolute pressure on the tail end, but you can certainly go above 1 atm stagnation pressure on the front end.

10. Feb 20, 2017

### jack action

I was thinking more on the line of removing the sticker with a vacuum. If air pushes on it, in the extreme case, you don't even need glue. The shear force caused by the air pushing on the frontal area (width X thickness), can that really be a factor?

My point was that if one could assume the frontal area is of significance when placed on the hood, it can become irrelevant if placed on the trunk where vortices can roll over the sticker. The actual flow could even be going rear-to-front close the rear window, just like the hair of the woman in the picture below: