Askham Grange, Ford Prison in West Sussex and five others can raise only 17 trained officers between all of them, supported by 26 lesser qualified staff – compared with more than 3,000 inmates, according to the figures released in the wake of the violence and destruction at Ford.
The POA's research says that on a typical nightshift Askham Grange has no senior staff, one prison officer, and two operational support staff to deal with a population of 123.
Inmates have included convicted murderer Tracie Andrews, who stabbed her fianc Lee Harvey to death and tried to pass the crime off as a road-rage attack.
Unveiling the numbers, POA assistant secretary Joe Simpson said they were "totally inadequate" and added that he was astonished the New Year's Day rampage at Ford had not happened before.
The riot broke out after officers attempted to breathalyse inmates for contraband alcohol.
It has raised concerns over staffing levels at open prisons after it emerged only two prison officers and four support staff were in charge of almost 500 prisoners.
The POA, which also warned inappropriate prisoners were being sent to open jails in an effort to cut numbers elsewhere, claimed there was a grand total of 43 staff in charge of 3,012 prisoners at all seven open jails, where inmates may be trusted to go to work in the community.
Mr Simpson continued: "We feel that's totally inadequate to deal with what we've got to deal with during the night. Sometimes prisoners come back in at all hours of the night as well. The problem with low staffing levels is that, if they've had a drink, they've got to be breathalysed because they're in breach of their licence conditions.
"When they're getting drink and drugs, and in some cases women – as it's been reported in the past – it's impossible for the staff who are on duty to cope. "
Prisons Minister Crispin Blunt said the inquiry into the "unprecedented" violence at Ford would look at the role played by staffing levels.
Mr Blunt said: "One of the issues will be about whether there are particular circumstances at Ford - to examine whether the staffing policies are appropriate at Ford compared to other open prisons. What we need to remember was that the incident was unprecedented.
"If something happens that's unprecedented, we've got to examine what the likelihood is of it recurring."
A Ministry of Justice spokesman said: "There are strict criteria for acceptance at open prisons, which exclude the most dangerous prisoners, and the type of incident that occurred in Ford open prison recently is rare.
"There are around 91 operational prison staff on duty overnight in open prisons, made up of roughly 65 trained and uniformed operational grade support officers and around 26 staff at prison officer grades.
"Such staffing levels have been risk-assessed as appropriate for open prisons."