Taxpayers paid for one scientist to have a bee sting his penis and paid other researchers to figure out that cheerleaders look more attractive in a group than individually, according to a painful new survey of wasteful spending released Tuesday by Sen. Jeff Flake.

At a time when the Obama administration is pleading for more money to fight the Zika virus, repair water pipes in Flint, Michigan, and combat the growing opioid epidemic, the ridiculous research projects suggest there’s plenty of room to save money already in the budget, Mr. Flake said.

Unnecessary projects included the $50,000 for researchers who studied femininity and masculinity in members of Congress. The National Science Foundation paid the University of California, Los Angeles to conclude that Republican women are feminine and Democratic women are not.

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The NSF also funded the bee sting study, and a majority of the 18 other projects Mr. Flake identified in his “Twenty Questions: Government studies that will leave you scratching your head.”

“It’s time that Washington set clear goals for federally funded research, improved transparency to ensure tax dollars are being prioritized to meet those goals and reduced wasteful and duplicative spending on lesser priorities,” Mr. Flake said.

The NSF didn’t respond to a request for comment Tuesday, but in the past has called its selection process the “gold standard,” saying it runs projects by panels of experts who decide what spending is most promising.

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Mr. Flake said it would be hard to justify the study on femininity of women in Congress — research that the UCLA authors dubbed the “Michele Bachmann effect” after the former Minnesota Republican congresswoman. They concluded that Republican men don’t need to appear more masculine because their policy positions already show that, but said for women — and conservative women in particular — femininity was clearly discernible.

Perhaps most stunning, they named names, saying Democratic Reps. Rosa L. DeLauro and Anna G. Eshoo were rated “less gender-typical,” while Mrs. Bachmann and Reps. Kay Granger and Cathy McMorris Rodgers were rated “highly feminine.”

The researchers said more studying is needed to “understand the roots of the GOP’s more feminine face,” but said it could be as simple as liberal Democrats aiming to diminish disparities between the sexes, while conservative Republicans hold positions “that tend to bolster traditional sex roles.”

Neither Ms. DeLauro’s office nor Ms. Eshoo’s responded to requests for comment on that use of federal money, but Mr. Flake said he hoped they weren’t happy with the spending.

“That’s a brutal one,” he said. “I thought it was pretty inappropriate, frankly, and I hope people are incensed by it and look a little more closely at what we’re spending our money on.”

Some of the projects singled out by Mr. Flake, Arizona Republican, have already been highlighted in the Ig Nobel Prizes, given by scientists to the more curious projects undertaken under the rubric of research.

Michael L. Smith’s bee sting study was a winner in 2015, drawing cringes from Ig Nobel judges who were astounded that he subjected himself to hundreds of stings across 25 different body parts, trying to gauge which hurt the most.

He said scientists had previously tried to rank animals’ and insects’ stings compared to one another, but nobody had calculated where on the body it was worse to get stung. While admitting that “pain is notoriously difficult to quantify,” Mr. Smith tried anyway — forcing honey bees to sting him from the top of his skull to the tip of his middle toe, both of which tied for least painful places. The penis turned out to be only the third-worst out of 25 options, falling behind nose and upper lip.

Mr. Smith admitted his study’s usefulness is limited because of “its low sample size: one person, the author.”

“Although these findings cannot be generalized, they are still interesting,” he insisted in his write-up of his research.

It wasn’t just the NSF that funded questionable studies. The National Institutes of Health — an agency that’s currently begging for more money to combat the Zika virus — paid for researchers to feed alcohol-laced grape juice to finches to see if the birds slurred their songs when inebriated.

The birds’ songs were “a bit less organized,” the researchers at the Oregon Health & Science University reported.

The Defense Department, which congressional Republicans insisted needs an injection of tens of billions of dollars this year, spent money to study why coffee spills when someone walks.

“In our busy lives, almost all of us have to walk with a cup of coffee. While often we spill the drink, this familiar phenomenon has never been explored systematically,” the researchers said in explaining their project to the magazine Science. The researchers concluded, as any parent already tells a child, that walking slower and steadier reduces the chances of spilling.

Mr. Flake said he hoped highlighting the bizarre spending choices would push bureaucrats to be more watchful in the future.

He also said it’s time to enlist the public. He introduced legislation to require the White House to develop a system to weed out duplicative research and to require agencies that fund research to post a summary, funding details and information about papers written for every unclassified study paid for by taxpayers’ money.