As you mention, a pineapple to the head is much like a potato to the head. (Wise words). It turns out that potato cannon injuries have been studied as they relate to the speed, weight, and diameter of the potato. The formula can be easily adapted to a pineapple.
The paper analyzing potato gun injuries is, "When backyard fun turns to trauma: risk assessment of blunt ballistic impact trauma due to potato cannons" (DOI 10.1007/s00414-011-0552-y ). I'm not sure I should link to this paper because of copyright issues, but you may have heard of a "hub" where you can find such papers.
This paper uses the Sturdivan Blunt Criterion (BC) formula. BC = ln(0.5 m v^2 / (W^(1/3) * T * D)). This gives a number that correlates to injury severity.
- m is the mass of the pineapple in kg, 1 kg
- v is the speed of the pineapple in m/s
- W is the mass of the target in kg. According to the paper W = 4.9 kg should be used for the head.
- D is the diameter of the pineapple in cm. A typical pineapple has a diameter of 15 cm, but the paper mentions a corrected formula for D should be used for head impacts, so that D = 7.5 cm.
- T is the thickness of the body wall in cm at point of impact. According to the paper T = 1 cm should be used for the head.
This would let us solve for v if we knew our desired Blunt Criterion value. For this, we can refer to "Tolerance of the skull to blunt ballistic temporo-parietal impact" (DOI 10.1016/j.forsciint.2010.10.023 ) which the potato gun paper also relies on for calculating head injury severity. According to this paper, based on the curve in Fig 9, when the BC value is 1.0, skull fracture is unlikely. When the BC value is 3.0, skull fracture is almost certain. The 50% chance of skull fracture occurs around BC = 1.7.
The potato gun paper lists four examples of head injuries from a potato gun. Three of the four involved skull fractures, but none were fatal. (In one of the four cases, the projectile remarkably was a frog rather than a potato). Also, the potato gun paper analyzed potato guns which all had head BC around 3.0. So BC=3.0 is high enough to produce a fracture but not high enough to reliably produce death. So let's pick BC=4.0 as our target.
So, we solve BC = 4.0 = ln(0.5 * 1 * v^2 / ((4.9)^(1/3) * 1 * 7.5)) for v. This gives v = 37.3 m/s, which is 83.4 mph.