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Some people develop fear of flying as a result of an incident, ranging from a crash to turbulence. Others appear to have it without previous exposure. It has been said that fear of falling, or of heights, is the only built-in human fear - this seems glib but a reasonable fear of aerial activities seems very common.
Several airlines provide or support anti-phobia courses, benefitting humanity and that subsection of it owning their shares. In general these are run as one would expect, starting with an effort to persuade people that physics and aerodynamics can be relied upon and progressing to graded exposure.
In the UK, calling British Airways - or better, as a first step in mastering their fear, empowering the patient by recommending that they call BA - is a reasonable default. See the BA web site for more details. A simulator-based service is also offered in Devon.
Five miles up is not a good place for your patient to discover they do not agree with a benzodiazepine! The crew also will not thank anyone for providing the means to become disturbingly disinhibited or disoriented enough to want to step out for a breath of fresh air. Providing the anxiety is not very severe, and the patient is able to check the effect and tolerability of the proposed sedative in advance at ground level, and is not travelling unaccompanied, a cautious exhibition of a sedative, as suggested in BA's own guidance, may be a proportionate, and kind, response.
Many flyers have resorted to a dose of alcohol, judged with more or less accuracy, and only a few of them have ended with disaster, however although both alcohol and other sedatives have disadvantages including a theoretical increase in risk of DVT from slumbering, the dehydrating effect of much alcohol, on top of that of dry cabin air, is better avoided.
The benefits of a long sea journey are often underestimated, and it has, besides, a smaller Carbon footprint.