A psuedo-scientific study...
How many heads do we really need to safely avoid a crew emergency
Conversely, how many do you need for crew happiness?
This is a question that crossed my mind back in the days when my family
all shared one bathroom in our little house.
I always suspected that having TWO bathrooms with a bunch of people was not TWICE as good, but EXPONENTIALLY better.
Three or more must just give diminishing returns.
("Better" in the sense of fewer emergencies where someone is pounding on the bathroom door in need.)
Now this question has come up regarding our cruising boat
and estimated guest count.
I think the average cruising crew count is often close to 2, but we plan on 4+ for longer passages.
Peggy Hall probably already has the answers, but here is a bit of math to explore this question in depth
The following analysis makes several assumptions and generalizations.
It does NOT consider male/female differences, and assumes nobody does their business top-side. (our boat
doesn't perfectly comply here)
An "emergency" means someone has to go, but all heads are occupied.
Also, it assumes worst-case: everyone is awake during the same 16 hours. (must be anchored!)
Nmins_in_day = waking hours (16) * 60 min/hr = 960 minutes in a waking day
Ncrew = crew count
Nheads = head
Ppee = probability of a person using head
= (16 min per day / 960 waking minutes) = 0.017
Nemergency = minutes per day of emergency
(note: 16 min per day in the head is taken from a British study of bathroom habits)
Nemergency = [(Ppee)(Ncrew)*(Ppee)(Ncrew-1)*(Ppee)(Ncrew-2)...(Ppee)(Ncrew-Nheads)]*Nmins_in_day
Here is a table of results for a crew count of 2-10 and a heads count of 1-4...
Nemergency (emergency minutes per day)
Yes, having 2 heads IS better than twice as good as having 1 head. With 4 crew, 2 vs 1 head is 29 times better!!
TWENTY NINE times the peace.
TWENTY NINE times the happiness.
However adding a 3rd head looks irrelevant until 8 or more crew is on board.
Interestingly, 10 crew with 2 heads will involve 3.2 minutes of door-pounding per day.
A further happiness study could include the opposing forces such as cleaning
,maintenance where FEWER heads would be better.
A fancy equation might not be needed to find the perfect number though.
2 heads looks like the ideal count for 3 to 7 crew according to the chart.