How can I measure whether a football passes through a hula hoop? The main challenge is the need for outdoor use, which presents difficulties due to the presence of ambient light (sunlight). It might be possible to install a sensor module on top of the hula hoop, which comprises a Class 1 laser emitter and a receiver. The emitter emits invisible laser pulses that bounce off any objects in the sensor's field of view, and the receiver detects the returning pulses. When a fast-moving object such as a football passes through the hoop, it will interrupt the laser beam, causing the sensor to detect the change in signal and register the event. I also explored the possibility of using infrared (IR) technology to detect the passage of a football through the hula hoop.
If you aim for absolute cheapness and an electromechanical solution fits your bill you could use microswitches.
Mount some microswitches on the hula-hoop and connect their levers to very light and rigid plastic strips that go from the microswitch to the center of the hula-hoop. When the football pass through the hoop it will momentarily displace one or more strips, that in turn would act on their corresponding microswitch. The strips should be so light that the football is not impeded in its motion through the hoop, of course.
The number of strips depend on the relative size of the football wrt to the diameter of the hoop. Probably 4 or 5 will do. You may have to tinker a bit and think of a way to fasten the strips to the hula-hoop (the other end would be flapping around near the center of the hoop) and how to make them act on the switch.
All this requires a bit of mechanical thinking and skills, but probably is unbeatable from a cheapness POV. You could get 5 microswitches for a couple USD and the other materials could also be recycled or commonly available stuff (for the strips I can think of electrician's cable ties, for example; when fastened to the hoop the part you usually cut-off is fairly elastic; there are quite long ones that could fit your application).
Moreover sunlight won't interfere at all. And if you don't need a particularly professional job, you can easily waterproof it all (after you test the set-up) with generous application of silicone sealant (silastic) and/or hot-glue.
In addition, since you don't have delicate electronic components, you could use common silastic for hydraulic applications, which would corrode components in the long run due to the presence of acetic acid in its formulation. The only parts you should protect are the terminals of the microswitches, where you would solder the connection wires. That's easy to do with some heat shrinks.
It's not an elegant solution, and aesthetically would probably look not too good, but its dirty cheap, especially if you have the skills to build it up, otherwise you could spend a lot of time to get it right (YMMV).
For this application, I would use a Time-of-Flight (ToF) sensor. This kind of sensor does not require any reflector, enabling the entire system to be contained on one side of the hoop.
Integrated circuits exist that implement ToF sensing, with a I2C interface that is easy to communicate with a microcontroller (be it an Arduino or otherwise). They automatically compensate for ambient lighting and work outdoors. Typical resolution for the distance measurements are would be 1mm, and supporting sampling rates of 25-90 Hz.
One alternative would be VL53L5CX, which gives a 8x8 array of distances. It has a 45x45 degree square FOV (65 degree on diagonal). It could be mounted either looking straight across the hoop, or slightly up or down. The processing would be able to look at the distance to the ball, as well as the shape. Official break-out boards are available for 20 USD. Or 10 USD for the cheapest from China. The chip costs 7 USD @ 100 pcs, and 5.5 USD @ 10k. Other array alternatives could be TMF8820/TMF8821 with 4x4 and 30 Hz sample rate. It is as low as 4.5 USD @ 10k units.
It may also be possible to use a single-channel ToF distance sensor. Those are down to 2 USD @ 10k. But due to the more narrow FOV, the sensor would have to be further away and look up/down into the hoop. This might increase total system costs by more than the available savings. Reliability might also be lower due to the inability to look at the shape of the object.