If it ain't fixed to the ground it ain't Business Real Property. An aeroplane fixed to the ground would be pretty useless I'd say.
If it was allowable and the use was incidental and trivial you'd get away with it.
The trustee of an SMSF can not be held accountable for poor investment decisions but I wouldn't go out of my way to lose money.
Best digging a hole in the ground and pouring money into it.
Your SMSF could own the asset and lease it to another party without concern, if it was used in your business it would be classed an in-house asset and be a major pain in the back end if it represented more than 5% of your funds assets.
Do not take this as financial advice, be sure it's appropriate for your needs, bla bla bla.