# Why should isobars be aligned with the leading edge of the main wing for a transonic cruiser?

When designing an airplane meant to cruise at transonic speeds (or supersonic speeds), I heard that one should look at the isobars on the main wing in order to assess if the shape, sweep angle and other airfoil parameters are suitably chosen. I also read that the better configuration yields isobars that are parallel to the leading edge. I already know that there are several techniques to get the isobars aligned with the leading edge (area ruling, adapting the sweep angle, extra care in the design of the junction between the fuselage and the wing), but why is this configuration better than another one? What does it improve?

I finally found several arguments to answer this question from different sources.

Sweep and Mach Number from Airbus

This argument is developed in an Airbus magazine from 1985. To grasp it it is important to understand the purpose of swept wing. By sweeping the main wings one introduces an angle between the leading edge of the wing and a line perpendicular to the fuselage axis. Let's consider two airplanes, one with swept wings (A) and one with straight wings (B).

One of the most important parameters is the Mach Number experienced by the wings. It is measured normal to the leading edge of the wing which means that for the two airplanes flying at the same Mach Number, the Mach Number seen by wings of (B) is larger than the one seen by the wings of (A). This allows to fly at higher speed because it delays the large increase in drag (drag divergence) and other effects linked to the Mach Number around the airfoil.

However, if the isobars on the wing are not aligned with the leading edge, they are following a less swept pattern which tends to reduce the benefits from the sweep angle of the main wing because the effective sweep angle is smaller and the Mach Number around the wing should not be computed normal to the leading edge but normal to the isobars close to the leading edge.

From a theoretical point of view it would even be better to have isobars not aligned with the leading edge but having a larger sweep angle. However this never happens due to boundary conditions at the root and the tip of the wing.

Other sources

All this is also explained here.

Finally, this last source deals also with the matters but does not justify the need for the isobars to be parallel to the leading edge. It deals more with the shock on the wing and the ways to weaken it and thus reduce the drag.

The aim of parallel isobars on the wing is to generate quasi two-dimensional flow.

Let's say, the layout is set. You shaped the wing in a way to 'force' the isobars to be parallel with the sweep - the entire span. You now (should) have the same pressure distribution in every single profile of your wing. This eases your calculations extremely!

• It obviously eases a lot the predictions and the computations but is there any aerodynamic advantage to use this? Does it improve the drag, the lift, some kind of moments and so on...? – Ludovic C. Dec 25 '13 at 17:47
• I don't think that this has a direct effect on drag etc. If someone knows better I'll retract everything and assert the contrary ;) – ClickOKtoTerminate Dec 25 '13 at 21:54
• @ClickOKtoTerminate: The two main advantages are no crossflow and the same critical $c_p$ over the whole span. Flow direction is orthogonal to isobars, and having the same spanwise pressure over the whole span will ensure that airflow is well behaved. Also, the same pressure means that the wing has an optimum thickness distribution and every part of it will have the same maximum Mach number. – Peter Kämpf Nov 15 '14 at 21:35