For this problem I$\text{'}$m $$supposed to $$iteratively try different X $$positions in $$steps from $0$ to $1$ to $$find the max thickness that gives the max lift on an $$airfoil$.$ I also need to $$find the thickness that gives the least drag. The first picture is $$given where, M is $$mach $3,$ H is $$the max thickness, and c is $$the chord length. The following pictures and process is my $$rough understanding of $$how to $$solve it$.$Picture $2$shows the general setup of $$the table that will tabulate the lift and drag for each x $$value$.$ Since M$>1$this is $$supersonic flow so $$there are shocks present. Because of $$this I need to $$obtain the angle Beta. First I obtained theta for x $=\mathrm{.}05$ by $$basic trig shown in $$picture $3$and then used the Theta, Beta, Mach Chart to $$get Beta for weak shock. This came out to be $22$degrees$.$ However I don't remember the process to $$solve after getting beta. I think you have to $$solve for the different pressures and I know you have to $$use the compressible flow tables. Then you plug the asssociated values into the lift and drag equations to $$get the answers. Picture $4$better illustrates the shocks. In $$picture $5$I vaguely remember combining the pressures to $$get a resultant force. Any help would be $$appreciated as $$I read my $$textbook and it $$isn$\text{'}$t of $$any help for this problem.