So I want to make this project, where I remake a shopping cart into a simple 'gokart', with a steering wheel, brakes, etc..
Now the main issue: I thought about using a fan for accelerating the cart, even though it seems rather unlikely that a fan will push such a heavy body.
I wanted to check, however, how big of a fan I would need to make it work. My question is: how to calculate the force which is exerted by a 'casual' fan? I just want to know how many Newtons a typical fan exerts.
Much will depend on the inflow conditions into and the outflow conditions of the fan. If both are free of obstructions, you can apply the static thrust formula for propellers, starting with the electrical energy the fan motor consumes. Next, use generous reductions for motor (90%) and propeller (40%) efficiency.
$$T_0 = \frac{P\cdot\eta_{Prop}\cdot\eta_{el}}{\sqrt{\frac{2\cdot T_0}{\pi\cdot d_P^2\cdot\rho}}} = \sqrt[\LARGE{3\:}]{P^2\cdot\eta_{Prop}^2\cdot\eta_{el}^2\cdot\pi\cdot \frac{d_P^2}{2}\cdot\rho}$$
If, however, you want to sit on your cart and have the fan spinning in your back, reduce expected thrust by half for a first-order approximation.
Nomenclature:
$\kern4mm d_p\kern6mm$propeller diameter in m
$\kern4mm P\kern7.5mm$Power uptake in Watt
$\kern4mm T_0\kern5.5mm$static thrust in N
$\kern4mm \eta_{Prop}\kern1mm$propeller efficiency
$\kern4mm \eta_{mot}\kern3mm$motor efficiency
$\kern4mm \pi\kern8mm$3.14159…
$\kern4mm \rho\kern8mm$air density in kg/m³
