The Rough Science base this year sits on the slopes of a magnificent mountain: Mount Kendall. And for this week’s challenge the team will have the task of getting to know this peak very well, working out how high it is and how much it weighs. Not just the part we can see sticking up above the Mill, but the root of the mountain, too, right down to the bottom of the Earth's crust. There’s a lot of maths to combine with some canny field geology to pull this one off and Hermione and Ellen pull together a unique blend of botany and geology to try and crack the dimensions Whilst the girls get to grips with the mountain, the boys are tasked with producing a pair of sun glasses to protect Kate from the glare of the Sun. At the altitudes they are working, the Sun is particularly glaring. Mike thinks he can make glass out of sand, but it’ll need Jonathan to build a furnace that can produce temperatures of over 1200oC for hours at a time. It’s not something Jonathan feels confident about, and it takes the whole of the first day to come up with a design for an oven that can get anywhere near those conditions. Even when Mike find a possible source of sand nearby, the prospect of making glass, let alone making sun-glasses still seems remote... Back on the mountain, in a combination of tree line mapping, clay model building, good old geological mapping and weighing their rock samples the girls are close to an answer for the mass of the entire mountain – roots and all. But with all their assumptions, estimates and the general inaccuracies of a flat-out three day attempt to survey an entire mountain how close will they get to the real figure?

• Kate Humble
• Iain Stewart