Loads of dinosaurs had wings, but not many of them could fly. There’s a dinosaur in your garden right now, probably the one that keeps stealing your chips, because a seagull is a dinosaur, and so is every robin, pigeon and chicken. Feathers turn up again and again across the dinosaur family tree, and most of them had nothing to do with flying. Oviraptors spread their feathered arms over their nests to keep their eggs warm, and some parents have been found still sitting on them. Others used feathers for showing off and for keeping warm in the cool forests of north-east China.

This week’s word is primaries. Hold your arm out: shoulder, elbow, wrist, hand. The primaries are the big, long, stiff feathers that grow from the hand, and they do the hard work of flying. Every bird that flies, from a hummingbird to an albatross, has between nine and eleven of them. So if you find a fossil wing, you can count.

Lauren and Cassius Morrison hear from Dr Jingmai O’Connor, Associate Curator of Fossil Reptiles at the Field Museum in Chicago. She explains why Microraptor, with feathers on its arms and its legs, probably glided down from the trees like a flying squirrel, and why Anchiornis, with a skeleton almost exactly like Archaeopteryx, has 30 primaries and probably couldn’t fly at all. She also owns up to getting something wrong. She once wrote that Microraptor couldn’t cough up pellets, then looked again at a Microraptor with a whole lizard in its stomach. A skeleton that size can’t go all the way through, so it had to come back up, and she is now writing a paper to say so. As she puts it, saying “I don’t know” is the most powerful thing a scientist can say.

Fresh from the Dig starts with Jingmai’s own brand new dinosaur, Jian changmaensis, a barn-owl-sized, four-winged cousin of Microraptor from about 120 million years ago in the Changma Basin in north-west China. It might finally explain the little bundles of smashed-up early bird bones found there for years. Then Yi qi, whose name means strange wing, a tiny dinosaur with bat-like skin wings that looked a lot like a mini dragon. And how scientists worked out the real colours of a dinosaur: Anchiornis was grey and black with white stripes on its wings and a rusty red crest, a bit like a woodpecker. In the Dino-Mite Question, Jonah, eight, from Glasgow, asks whether a chicken nugget is a dinosaur nugget. It is. And the wishbone in your roast chicken is the same bone you’d find in T. rex.

Then it’s Build a Dino Lab. Week seven is the arms: four wings like Microraptor, or feathered arms only with bare scaly legs underneath. Lauren picks feathered arms with seven primaries and no leg wings. Seven is two short of what you need to fly, and that’s fine, because this dinosaur was built to run, big feathers on its legs would trip it up, and it’s already carrying a heavy tail, plates and a thagomizer. Jingmai would have chosen the same. Next week, our dinosaur gets a nose.

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A dinosaur’s tail could be a third of the whole animal, about as heavy to lug around as a concrete block, and for well over a century people drew dinosaurs dragging theirs along the ground. They didn’t. Palaeontologists have found thousands of dinosaur footprints and almost no tail marks, so a healthy dinosaur held its tail up and out behind it. The tail-dragging monsters in old paintings and old films were what scientists thought at the time, and that’s fine. Being wrong and then finding out is how science works.

This week’s word is counterbalance. It’s the seesaw, the tightrope walker’s long pole, and the heavy block on the back of a tower crane that stops it tipping over. A long tail stopped a two-legged dinosaur falling flat on its face. But a crane’s counterweight just sits there, and a dinosaur’s tail didn’t. Underneath it ran an enormous muscle, a giant bottom muscle, that ran forwards from the tail and down on to the thigh bone and pulled the leg back with every single step. So the tail was a counterbalance and an engine.

Lauren and Cassius hear from Pasha van Bijlert, a PhD researcher at Utrecht University in the Netherlands, who builds dinosaurs inside a computer and teaches them to walk. He 3D-scans a skeleton, adds muscles using the rough patches where they once gripped the bone, then drops the whole thing into a physics simulator that works out for itself how to walk and run. To check it works, he built an emu the same way, as if it were a fossil, and it topped out at about 40 kilometres an hour. Then he went to the Australian outback to film real emus with drones, and two of them ran alongside the car at 45 kilometres an hour and simply kept going.

Fresh from the Dig starts with Pasha’s own team, who worked out how fast Tyrannosaurus rex walked from the way its tail bobbed. Everything that swings has a rhythm it prefers, like a playground swing, and the rhythm of a T. rex tail gives a walking speed of about four and a half kilometres an hour. That’s your walking speed too, which is not a reason to go for a stroll with one. Then Stegouros from Chile, a small, cute armoured dinosaur whose tail ended in seven pairs of flat bony plates locked together like a fern leaf, and was about as friendly as an Aztec war club. And the footprints that settled the tail question turn out to be trace fossils, the same family as fossil nests, last meals and dinosaur poo.

Then it’s Build a Dino Lab, where one real fact becomes one real piece of the perfect dinosaur. Week six is the tail: a long, heavy, muscular one held out straight, or a light little stump like a pigeon’s. Lauren picks the long, heavy tail held off the ground, because episode one promised this dinosaur could run, and without it there is nothing to swing the thagomizer. Next week, wings, for a dinosaur that can’t fly.

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The dinosaurs had around 160 million years on Earth, so there was never just one dinosaur climate. There were deserts, volcanoes and jungles, and there were forests at the North and South Poles, because for most of that time there was no permanent ice anywhere on the planet. Britain was subtropical to tropical. If you were packing for a trip, you would want a raincoat and an autumn jumper, not a snowsuit.

This week’s word is super greenhouse. A greenhouse lets the sun’s heat in through the glass and makes it hard for it to get back out, and carbon dioxide in the air does the same thing to the whole planet. In the super greenhouse of the Cretaceous there was far more of it, sea levels were so high that a seaway split North America down the middle, and temperatures in some places may have reached 40 to 45 degrees. That is hotter than a hot bath.

Fresh from the Dig is all about where dinosaurs lived. The dinosaur highway in Oxfordshire, a 150-metre run of tracks made by long-necked sauropods and the meat-eaters following them, was laid down in a warm, muddy lagoon, exactly the kind of ground that holds on to a footprint. The Carnian Pluvial Episode, roughly two million years of rain in the Triassic, spread forests across the hot, dry supercontinent of Pangaea, and it is one of the leading ideas for why dinosaurs took over. And in northern Alaska, inside the Arctic Circle, palaeontologists have found baby dinosaurs far too young to have migrated, which means dinosaurs lived there all year round, through months of darkness and months of midnight sun.

Lauren and Cassius are joined by Professor Kirsty Edgar, a micropalaeontologist at the University of Birmingham, whose fossils are smaller than a grain of sand. She studies foraminifera, tiny plankton that build shells in the surface ocean and have been doing it for hundreds of millions of years. The oxygen in those shells comes in a lighter and a heavier form, and the mix a shell takes up depends on how warm the water is, so each one is a thermometer that never knew it was a thermometer. When they die the shells sink and pile up on the seabed in layers, oldest at the bottom. Kirsty has spent two-month research voyages drilling that seabed, from Tahiti to Hawaii and from Tasmania round to Perth, one of which set off straight into the tail end of a Southern Ocean storm.

Otis, who is six and from Cardiff, wants to know whether he could have gone swimming in a 45-degree sea. Sadly not: a warm swimming pool is about 30 degrees, a hot bath is about 40, and anything else in the water would have been bigger than him and a better swimmer. Then it is Build a Dino Lab, where one real fact becomes one real piece of the perfect dinosaur. Week five is skin, and Kirsty’s advice is to make it pale, for the same reason a white T-shirt keeps you cooler than a black one. Lauren picks skin that reflects the sun, even though it makes the dinosaur easier to spot, because with a thagomizer and steak-knife teeth it can look after itself, and nobody wants a dinosaur that cooks. Next week, a tail. Probably.

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