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We fabricated nonimpregnated HTS superconducting coils with a BSCCO tape. Bobbin materials in the coils are a Dyneema(R) fiber reinforced plastic (DFRP) and a glass fiber reinforced plastic (GFRP). We excited those coils with ac currents, and estimated mechanical losses. According to the measured data, the mechanical loss decreased with increase of winding tension of the coils, because strong winding tension fixed the coils tightly. Also, the mechanical loss occurred in the DFRP coil was smaller than that occurred in the GFRP coil. A thermal expansion coefficient of the DFRP is a negative value, that is, the DFRP expands with cooling down from room temperature to cryogenic temperature. The expansion of the DFRP bobbin made the winding of the coil fix tightly, and the mechanical loss decreased. From those experimental results, we think that the DFRP bobbin is useful for decreasing of mechanical losses of the ac coils.