How can we calculate the benefit gained from taping glider wing roots?

Question

Most (all?) glider pilots will be familiar with the practice of taping wing roots. As most of the gliders in my glider club (and I would guess, in the world) are stored with the wings detached, the practice of taping wing roots to close the gap between the wing and the fuselage is one which is hard to get through glider training without learning. Indeed, even the type/brand of tape used can be a subject of hot debate. This picture shows what a taped wing root looks like:

I've always wondered though how critical this practice is. The gap in wing roots, once spar pins have been inserted, is typically pretty small. I've forgotten to tape, but I usually don't forgot, partly because I know someone in the club will point out that I've forgotten and a fresh debate ensues. I would say I'm currently skeptical (but open minded) about the benefit of doing this.

Question:

How effective is taping wing roots?

Lets take, for example, the Schempp-Hirth Open Cirrus, which has a published maximum glide ratio of 44:1. Lets assume this glide ratio was calculated with the wing roots taped. This assumption is bolstered by the fact that the rigging check list (Open Cirrus Flight Manual, Page 20) has taping the wing roots as a step. What would the glide ratio be reduced to if the wing roots are not taped? I do understand that the answer would depend on the width of the gap. Lets assume that is 1/16th inch (1.5 mm) for this example.

Secondary Question:

What would the answer to the same question be applied to the gap tape used between the aileron and the wing, as is shown in this picture:

Answer 1

The two questions actually concern very different issues.

The second question is easier to answer. Let's take your thought on:

I've always wondered though how critical this practice is.

It is pretty crucial! If you did not tape the gap between the wing and the aileron, you increase chances of a stall. This is especially true at low speed and large angles of attack, i.e. while thermaling or landing. Then an airflow from the lower side of the wing to the upper side might occur, through the gap, destroying the upper side's airflow. This very certainly leads to a performance penalty but also favors stalls. There have been some prototypes experiencing exactly this loss in performance (I could provide more detailed references if desired). I haven't heard of a stall related to this issue, and it actually might be unlikely to happen because under the described circumstances the transition point from laminar to turbulent flow is rather close to the wing's leading edge anyway. Nonetheless, the possibility of increased stall probability should be considered and, imho, is reason enough to never ever fly without aileron tapes.

The first question can only be answered qualitatively, at least with today's methods. It is effective: the airflow, although transitioned to turbulence by the tape, is definitely less turbulent than without the tape. Any kind of turbulence model will consider the "amount" of perturbation, i.e. larger discontinuities of the surface lead to stronger turbulence, thus more drag. You could fly with only one wing taped and see if you can notice a difference. If you notice rolling or yawing, then that's in favor of the corresponding wing. Honestly speaking, I doubt anything can be noticed if the wing consists of one part only, because the asymmetric drag is so close to the center of gravity (only at wing root). But if the wing is made of multiple parts, that might actually lead to some practical result. I am thinking of, e.g., Schleicher's ASW 28 or ASG 29 that have inner and outer wing parts + winglet, meaning 3 tapes distributed over the half wingspan. However, please check the manual of the glider first, if flying without tapes is permitted by the manufacturer.

And then there is also the noise issue.

Given all this information on the one hand and comparing it to the cost of tape and the time it takes to apply it, there is no reason not to use sealing. (Except, of course, around the canopy. You wouldn't expect what kind of ideas people can come up with)

Answer 2

Based on what I have heard, the difference makes up for about 1 or 2 glide points.

I can imagine that this does also play an important role to interference drag between the fuselage and the wings. Interference drag means that the sum of the drag forces of the wing alone and the fuselage alone will mostly be a lot less than the drag of the components when assembled as a whole system. That is because the airflows around the object influence each other.

Interference drag

If the gap is very close to the fuselage like it is on the Astir Cs for example, I can imagine not taping might play an even larger role on interference drag. In that case the gap will be inside the boundary layer of the fuselage and all the accelerated airflow going alongside the fuselage will pass through that critical area on the wingroot. That would make up for a drastical increase in total drag force.

Induced drag

An airflow from the lower to the upper side of the wing would also, besides from promoting a stall, cause an increase in induced drag as the air will try to even out the pressure differential from both sides of the wing by passing through the gap.

Parasite drag

Lastly the parasite drag in general will increase as the flow around a seam parallel to the airflow is especially bad for performance. Along such gap the airflow will be very turbulent as many vortices will form resulting in a higher drag force.

For that reason sailplane manufacturers are trying to avoid gaps parallel to the airstream. This can be seen when comparing the shape of modern plane's canopies to that of older designs.

To the second Question

In this case the gap is perpendicular to the airflow. So actually not as bad as if it would be parallel. In this case however, the tape tries to ensure that the airflow over the wing stays laminar for as long as possible which can only be obtained by a very smooth surface that the airflow can follow without separating from the wings surface and without forming vortices. Laminar flow causes significantly lower drag than turbulent flow does. Once the flow is turbulent though it will not become laminar again that quickly. So it is important to keep that from happening in the first place.

Interestingly supporting the flow at or shortly after the separation point to form vortices and to become turbulent can actually delay airflow separation and reduce drag. That is why some planes use zigzag shaped transitions to the ailerons acting as vortices generators. In case you ever wondered why there is zigzag tape shortly before the trailing edge of some glider wings and elevators.