The American Museum of Natural History in New York will unveil an exhibition of the world’s largest dinosaurs this Saturday. Some visitors may wonder how the creatures could ever eat enough to sustain their size, but the Explainer’s mind is in the Jurassic gutter. How did those monsters manage to have sex?

From behind, probably. Paleontologists know very little about how dinosaurs mated, because soft tissue rarely appears in fossils. (They figured out how to determine dinosaur gender only a few years ago: Females had a special calcium reservoir to help with eggshell formation.) It is highly probable that dinosaurs had a cloaca—as do most birds and reptiles—which is a single opening for urination, defecation, and reproduction. If that’s the case, we might speculate that the male and female would have aligned their cloacae such that the male’s penis could emerge to penetrate the female cloaca. (It’s also possible that dinosaurs had no penises, and, like some birds, reproduced by squirting semen from one cloaca at another.) Modern ornithologists and herpetologists call this a “cloacal kiss .” Beyond that, it’s all conjecture. Paleontologists can only guess about mating positions, duration, and behavior. The majority view seems to be that large males like the Mamenchisaurus—a 60-foot-long behemoth featured in the new exhibition—probably mounted from behind, like modern giraffes and elephants.

There was probably a courtship ritual among dinosaurs, involving signature body features. Last year, a group of paleontologists showed that the headcrests of pterosaurs and enormous fins on the backs of pelycosaurs were most likely there to attract mates, because they seem to have grown larger and larger through the generations. * Similarly, some researchers think sauropods like the apatosaurus (which was once called the brontosaurus) grew long necks for mating displays rather than to reach the high leaves. Male triceratops may have locked their massive horns for the right to mate.

Unfortunately, we know almost nothing about the size of other, more intimate dinosaur parts. The ratio of penis length to body size varies so widely among dinosaur relatives that it’s hard to make a solid guess about a dinosaur’s endowment. Some ducks, for example, are just a couple of feet long, but have 7-inch penises. On the other hand, crocodiles that grow to 15 feet sport just a 4-inch organ. If you applied those ratios to the 40-foot-long body of a Tyrannosaurus rex, you’d get a penis of anywhere between 10 inches and 12 feet.

Paleontologists have spent a lot of time musing about dinosaur sex positions, and they can’t agree on very much. For example, even though sex for large, long-necked dinosaurs probably looked something like giraffe mating, there’s a dispute as to what the male did with its head. Some researchers believe he couldn’t have maintained adequate blood supply to the brain with it so high off the ground, so he must have gotten into some kind of high-pelvis, low-neck position. Others believe he could have held his head up high and proud during his few moments of glory.

Then there’s the weight issue. While elephant females are perfectly capable of supporting a good portion of the male’s 15,000 pounds, the largest dinosaurs weighed 100,000 pounds. For that reason, a small number of paleontologists believe the larger species probably had sex in the water, where the male’s buoyancy would take some stress off his partner.

The rear-mount hypothesis has its detractors. Some point out that neither elephants nor giraffes sport long, thick tails to obstruct male access. Others note that the spikes, spines, and plates that some females had all over their backs would have made the position unpleasant or impossible. These paleontologists suggest that the dinosaurs may have laid down on their sides and mated belly-to-belly. Or they could have faced opposite directions and backed into each other. The male may even have rested three legs on the female and wrapped his tail under hers.

Got a question about today’s news? Ask the Explainer.

Correction, April 15, 2011: The original stated that both species had fins. In fact, only pelycosaurs had fins, while pterosaurs had head crests. (Return to the corrected sentence.)