The underlying concept in the Dyson fan may be considered similar to that called: 'Trompe' (See Wikipedia), where a jet of water drags a flow of air. You can have a look in ESPACENET at Patents FR935340: 'Flow enhancer for jets and compressors'; US2946540: 'Jet propelled aircraft'; CA611861, for a 'Flying Disc', all by Henri Coanda, and US2918233: 'Aerodyne', by Alexander Lippisch, all in the same line, thus, I'd consider as best option to accept or reject Dyson fan as an alternative to propellers, ducted fan, or turbofans, conducting some experiments, with the design adapted to propulsion, not cooling or moving air, the Dyson fan data provided in a link in answer by JollyJoker is promising. Not?
The concept in Dyson fan was in some aircraft designs, the Avro Canada Flying Disc never went airborne and was uncontrolable, but the P Moeller disc m200x -YouTubehttps://youtu.be/3MwxVAZuFOs - flew with multiple fans, and was transposed into a toy named: 'Magic UFO', a variant drone.
See patents: US3065935, J Dubbury; GB383408, C E Johnson; US3022963, JCM Frost, showing the concept in Dyson fan was considered in Aircraft, calculations and experiments have the last word, but if an arrangement moves more air, meaning more mass, at similar speed, meaning more thrust, and this done with less power, men, you have an idea worth testing at airplane scale. Salut
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