Measurements of wind direction are sought after by a multitude of professionals in many different domains. Whether to recalibrate meteorological models or simply for leisure activities, the demand for accurate and responsive wind measurements is widespread. This study was motivated by the need to improve the responsiveness of direction measurements on yachts. Here we argue that the ideal form factor of the wind sensor can be determined using digital tools, rather than empirically, with the aim of improving the mechanical response of the wind vane. Then we present the results obtained by applying a predictive filter method tailored to the specified form factor. We have developed and experimentally validate a mathematical model describing the dynamic behavior of a wind vane. This model is then used to determine the form factor of the vane that will give the best possible response to perturbations it will encounter. To do so we use operational research tools, specifying the mechanical characteristics of the vane and by providing the future use conditions of the sensor, in the form of a wind speed spectral density. The design built from this optimization methodology helps reduce the response time of the vane by 44% compared to to designs currently in use. We then work on digital signal processing by using a predictive filter which takes into account the dynamic characteristics of the vane previously determined by the mathematical model. This step vastly improves the quality and sensitivity of the signal, leading to another reduction in response time of 83%. This brings the total decrease in response time at 90%. There is therefore not only an improvement in the quality of wind direction measurements, but also with respect to the set of data that is derived from this information. In the context of single-handed racing boats, the performance of the automatic pilot directly benefits from this improvement in responsiveness.