# Aerospace Validity and assumptions in the use of hyperbolic secant function for wake survey

1. Dec 29, 2011

### alchemist

Hi guys,

I have been trying to measure the drag characteristics of a wind tunnel model by using a pitot-static tube set up. From which the transducer will output to me the stream-wise velocity profile based on the pressure differential measured.

Following which, in order to evaluate the drag coefficient of the model, i have used the common method of fitting the velocity profile using a squared hyperbolic secant function. However, i realised that across all the different profiles measured, there shoulder of the profiles do not seem to be able to fit nicely into the hyperbolic function.

I would like to know if this is usually the case, or is there any other underlying assumption in the usage of hyperbolic secant functions which is not being considered here? For my case, the reynolds number of the flow is around 500k, is this an issue?

thanks!

2. Dec 29, 2011

Why are you constrained to use a hyperbolic secant function? For that matter, why are you fitting any sort of function to your data? You shouldn't need to do that at all. Unless I am misunderstanding your motives, you are ultimately trying to determine the total momentum lost in the fluid as a result of the model, which can be done by comparing the incoming velocity profile to the wake. You don't need to fit a function to do that.

3. Dec 29, 2011

### RandomGuy88

Getting drag from a wake survey is very simple and curve fitting is unnessesary. Take a look at "Low Speed Wind Tunnel Testing" by Pope.

When doing a wake survey the drag you measure can vary greatly along the span of the object. Meaning you get a different value depending on where you survey the wake. This is a bigger problem at low Reynolds number, and 500k is pretty low. So you will need to take measurements at several different locations along the span of your model and average them.

4. Dec 31, 2011

### alchemist

well, i understand where you guys are coming from, but the thing is that due to the nature of the measuring equipment set up, the data points on the velocity profile do not form a perfectly smooth profile, caused by random fluctuation (wind tunnel speeds, pitot tube calibration uncertainty) hence the use of a curve fit will remove such issues.

Basically the whole point of having a curve fit here is to allow for integration of the wake profile to determine the drag coefficient of the model. Which cannot be done by just taking the discrete data points.

5. Jan 1, 2012

### RandomGuy88

How significant is the deviation from a smooth curve? Due to experimental uncertainty these curves are rarely perfectly smooth. Does increasing your sampling time improve the curve? If the deviation is small you don't need to worry because the integration will take care of it, if the deviations are large there may be something wrong with the experiment. What object are you trying to measure the drag of?

6. Jan 2, 2012

### alchemist

Well, the deviation is roughly 1.2~1.5%, i am not sure how significant is this deviation, based on literature review, it should lie around 0.5%. i am just trying to measure the wake profile of an simple airfoil model.