If I could just find it in writing.
That's one's easy...
From a 1992 Opinion:
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Student pilot
With respect to Ms. Frame's operation of Mr. Turel's balloon, you stated that she holds a Student Pilot Certificate, that she uses the time she operates his balloon to pursue her Private and Commercial Certificates, that he allows her the use of the balloon at no cost, and that he instructs her to operate the balloon in high visibility areas for the purpose of advertising "Columbia Bookkeeping Services."
Section 61.89 of the FAR would apply here. The relevant provisions read:
(a) A student pilot may not act as pilot in command of an aircraft...
(3) For compensation or hire.
(4) In furtherance of a business.
Given what you described, we would be of the opinion that this operation would be in violation of sub-section (a)(3) of FAR § 61.89.
The FAA has historically taken the position that building-up flight time is a form of receiving compensation when the pilot does not have to pay the cost, or pays a reduced cost, of operation. We would also be of the opinion that Ms. Frame's operation would violate sub-section (a)(4), in that the advertising function of her operation furthers Mr. Turel's business.
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Let me reiterate the FAA's position regarding a private pilot's accumulation of flight time.
If that pilot accumulates flight time, the FAA considers free or reduced cost provision of the aircraft to be compensation, and the pilot is, thus, acting as PIC for compensation. This applies to all aircraft operations, including glider towing and lighter-than-air and hot-air balloon operations. Therefore, those operations would be prohibited unless they fall within the exception in FAR § 61.118(a).
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And from 1990 (this one it pretty famous as these things go - it involves a private pilot towing gliders. And, while the result was changed by a later regulatory amendment (now 61.113(g)), the principle remains:
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The second prong of Section 61.118 says that a private pilot may not, "for compensation or hire, act as pilot in command of an aircraft." There is no question that the pilot of the tow plane is acting as pilot in command of an aircraft. The issue is whether he is so acting "for compensation or hire." With regard to this second prong of Section 61.118,
the agency has repeatedly taken the position that building up flight time is considered compensatory in nature when the pilot does not have to pay the costs of operating the aircraft and would, therefore, be deemed a form of "compensation" to the private pilot under Section 61.118.
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BTW, before a numbering chenge, what is now in 61.113 was in 61.118.