The affix ac comes after the word ardhavan preceded by an upasarga (Preposition) in a compound.,
Thus प्रगतोऽध्वानं = प्राध्वो रथः, प्राध्वम् शकटं, निरध्वम्, प्रत्यध्वम् ॥
Why do we say \when preceded by an Upasarga\? Observe परमाध्वा, उत्तमाध्वा ॥,
उपसर्गाद् अध्वनः
Adhyāya 5 · Pāda 4 · Rule 85