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might get bogged down but big ones with longer legs might be able to walk, with their feet sinking to the firm ground.

There is another complication. Different soils support loads in different ways. Wet clays depend mainly on cohesion between the clay particles, and the load they can support is about proportional to the area carrying the load. Dry sand depends mainly on friction between the grains and the load it can support is about proportional to the 1.5 power of the area: that means that four times the area can support eight times the load. Our big dinosaur would be more likely than the small one to get bogged down in wet clay, but the danger of sinking in dry sand would be about the same for both.

Real animals of different sizes are not the same shape, like these imaginary dinosaurs. Table 3.1 shows masses and foot areas of various animals, based on the best data I can find. Here is how the table works. The mass of a particular Apatosaurus was probably about 35 tonnes or 35,000 kilograms (table 2.2). Its weight (mass multiplied by gravitational acceleration) was therefore 35,000 x 10 = 350,000 newtons or 350 kilonewtons. Some of the biggest known sauropod footprints are about the right size to have been made by it. The area of each fore footprint is 0.16 square meters and that of each hind print is 0.43 square meters, giving a total (two fore and two hind feet) of about 1.2 square meters. When the animal stood, this area supported 350 kilonewtons, so (weight/area) was 290 kilonewtons per square meter. It is easy to

FIGURE 3.4. Footprints at Davenport Ranch, Texas, redrawn from Bird (1944). The rock was formed in the early part of the Cretaceous period.

FIGURE 3.5. Rear views of (a) a lizard; (b) a bird; and (c) a mammal, and their footprints.

calculate that 1.2'5 is 1.31 (use the y" button on your calculator) so weight/(area)'s was 270 kilonewtons per cubic meter.

The other data in the table have been calculated in the same way. The Tyrannosaurus footprint area comes from smaller theropod footprints, scaled up to match the feet of the skeleton that was used for estimating body mass. The Iguanodon area comes from much clearer prints than the ones shown in figure 3.6.

Look at the values of (weight/area) in table 3.1. They tell us about the danger of getting stuck in wet clay soils. In general, we expect bigger values for bigger animals, as the argument about the two dinosaurs showed. Nevertheless, the value for elephants is lower than for cattle because elephants have relatively large feet. The values for Tyranno-saurus and Iguanodon are about the same as for cattle, so these animals would have been just about as good as cattle, at crossing soft wet clay. The value for the huge Apatosaurus, however, is about twice as high as for cattle. Apatosaurus might have got bogged down on ground that was safe for cattle.

Another possible comparison is with off-road vehicles such as tractors and military tanks. Various tanks of 37-51 tonnes (a little heavier than Apatosaurus) have peak pressures of 200-270 kilonewtons per square meter, under their tracks. These seem close to Apatosaurus'

value of 290 kilonewtons per square meter until you realize that Apa-tosaurus would have to lift its feet in turn when it walked. Peak forces on the feet of people and animals during walking are generally about double the standing values. The pressure under the feet of Apatosaurus must have reached 580 kilonewtons per square meter, when it walked. It seems that the dinosaur would be less good than a tank at crossing soft ground.

Now look at the values for weight/jarea)'s, which tell us about the danger of sinking in dry sand. In this case we have to be careful about our comparisons. Equal values mean equal danger of sinking only if the animals have feet of about the same shape, and the same number of feet. Apatosaurus, elephants and cattle all have four, roughly circular, feet, so comparisons between them seem fair. Apatosaurus has a higher value than elephants but a much lower one than cattle. It would be much less likely than a cow to get stuck in a sand dune.

Most real soils have properties between the extremes of wet clay and dry sand.

Fossil footprints can also tell us about the speeds of the dinosaurs that made them. They cannot tell us as certainly as if we could watch dinosaurs running and time them with stopwatches, but they can give us estimates that are probably fairly reliable.

When people walk slowly they take short strides. When they walk faster they take longer strides and when they run they take still longer

FIGURE 3.6. (above) Iguanodon bernissartensis walking with its fore as well as its hind feet touching the ground and (below) footprints which it may have made. From Norman 1 980. Both the skeleton and the footprints are from early Cretaceous rocks.

strides (figure 3.7). Notice how stride length is defined: it is the distance from one footprint to the same point on the next print of the same foot. Figure 3.8 shows stride lengths and speeds for human adults. If you find a set of footprints you can measure the stride length and use this graph to estimate how fast the person was going.

The same graph shows the same thing for some animals. The faster they go, the longer their strides. Watch an adult walking with a small child. The adult takes a few long strides while the child takes a lot of short ones. Similarly, small animals take shorter strides than large ones, at the same speed. Dogs take shorter strides than camels (figure 3.7).

Does this mean that to estimate speeds from stride lengths we need separate graphs for each species, and separate graphs for adults and young of each species? If that were true, dinosaur footprints could tell us nothing about dinosaur speeds because we could never get the data for the special graphs for dinosaurs. Fortunately, it seems not to be true. There is a general rule that applies to birds and mammals and probably also to dinosaurs. It seems better to compare dinosaurs to birds and mammals than to modern reptiles, because dinosaur footprints show that they walked with their feet well in under the body (figure 3.5).

How then should we look for a general rule? What we want to do is to make a graph like figure 3.8 that will apply to animals of different sizes. We expect long-legged animals to take long strides and short-legged animals to take short ones, so it seems sensible to calculate relative stride lengths relative stride length = (stride length)/(leg length).

TABLE 3.1 Data about the danger of getting stuck in soft ground.

WEIGHT WEIGHT

TABLE 3.1 Data about the danger of getting stuck in soft ground.

WEIGHT WEIGHT

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