Sheikh `Abdul-Majeed Subh, a prominent Azharite scholar, states: “The acceptance of every prayer is conditioned to be preceded by purity among other conditions. Hence, as for the ablution, practically speaking, one can perform ablution in the WC of the plane even though it may be small. Otherwise, one can make dry ablution (tayammum) on a few drains of sand we take in a purse before boarding the plane.
As for prayer, one can combine between Zuhr and `Asr in the time of Zuhr or `Asr and between Maghrib and `Ishaa’ in the time of Maghrib or `Ishaa’. We can also shorten the prayers which means that, one can perform Zuhr, `Asr and `Ishaa’ as two rak`as each. As for Maghrib, it has to be performed as three rak`as and Fajr as two rak`as.
As for the Qiblah (the direction to which one turns his face in prayer), the line of the plane may be available and thus we can realize the direction of the plane and the qiblah by that method. The direction of the qiblah in this case is dhanni (speculative) and not definitive (yaqini). It is permissible in this case to pray towards a speculative direction. One can also ask the host about the direction.
If the traveling period is not long, then one can combine prayers in the way we mentioned before riding the plane or on the transit place or after taking off the plane.