Dubins TSP NP-hardness proof detail
Not multiplying by $2Cn/\delta$, does not result in 


  ... Exact Cover having no solution if the optimal DTSP tour has length at least $L+\delta+Cn$.


It in fact would result in a length at least $L+\delta$. This length is not always greater than $L+ Cn$, hence the need to multiply all distances by $2Cn/\delta$, after which one obtains the authors' result : $2CnL/\delta+2Cn$.