MONSOON LOGIC: A New Method for Testing Ancient Sailing Itineraries Through the Formula Sailing Duration + Waiting Time = 6 Months - Reassessing Marco Polo's Sumatran Itinerary and the Aceh Impossibility

This paper introduces a new method for testing ancient sailing itineraries: MONSOON LOGIC (Adri, 2024, Copyright No. 001325735). The core formula is Sailing Duration + Waiting Time = 6 Months (Six-Month Rule), formally T_sailing + T_waiting = 6 Months for one monsoon cycle at one Turning Point. The method assumes that each sailing from a point starts at the beginning of the monsoon wind. Theoretically, sailing from China to India could depart not at the beginning of the monsoon. If departing in the second month, arrival at the Southern Turning Point in the third month of the monsoon cycle, waiting time is only 3 months at the Southern Turning Point, not 5. This could be an option for Chinese sailing ships. However, sailing is not just about saving sailing time but also business considerations and needs for ship repair and provisioning. Stopping in Sumatra could mean marketing Chinese ceramic products and silk, ship repair, and shopping for basic necessities for the journey to India and other western regions. From China to India, ancient sailing encounters 1 Turning Point: the Southern Turning Point, located in the corridor from the tip of the Malay Peninsula to the Kampar or Siak estuaries. According to the critical edition of Marco Polo: "When you leave the Island of Pentam and sail about 100 miles, you reach the Island of Java THE Less" (Polo, 1903, Vol II, Chap IX, p.284), noted as "Java the Less is the Island of SUMATRA" (Yule & Cordier, 1903, p.284, Note 1), and "when you leave the kingdom of Basma you come to another kingdom called Samara... was detained five months by the weather, which would not allow of his going on" (Polo, 1903, Chap X, p.292-293). Yule-Cordier interpreted this as "Samara, Sumatra Proper" (1903, p.292, Note 1), which became the Aceh narrative (Brill citing ii 284 ff; Larner, 1999; Facts and Details: "Polo remained in Samudra for five months"). Applying Monsoon Logic, we recalculate: A 13th-century vessel with Northeast Monsoon from Quanzhou has a 30-day radius of 2,700-2,900 km (80-120 nm/day). Quanzhou to Kampar-Siak = 2,700-2,900 km (possible), Quanzhou to Aceh = 3,800 km (impossible). Thus one month sailing only reaches Southern Turning Point, not Aceh. This supports Chinese chronicle: "Each fleet had to wait for up to four months in a port on the north Javanese or east Sumatran coast, or at Melaka, in order to catch the east-west monsoon" (Mills, 1970; Dreyer, 2007) and "ancient Lamuri was used as a staging post for traders waiting out the winter monsoon" (Ma Huan, 1433, Yingya Shenglan). The Aceh impossibility is twofold: (1) Impossible to reach within one month, and (2) Impossible to depart to India after 5 months because wind reversed. Corrected understanding: After waiting 5 months at Southern Turning Point (T_sailing 1 month + T_waiting 5 months = 6 months for first cycle), vessels sail with SE-NW monsoon to India in the second cycle, estimated 3-6 months. Therefore total duration China to India is 9-12 months, not 6 months. Alternative scenario: departing month 2 arrives month 3, waiting only 3 months, total 7-10 months to India, possible but business considerations (marketing ceramics/silk, repair, provisioning) made 5-month stop in Sumatra economically rational. Barus Paradox is also revised: China to Barus (Fansur, Polo, 1903, Chap XI, p.299) requires 2 Turning Points (Southern Turning Point + Northern Tip of Aceh). China to Southern TP = 6 months (1+5), Southern TP to Northern Tip = in second cycle (1-2 months), waiting again at Northern Tip because wind still SE-NW when arriving, needing another 6-month cycle to turn south to Barus = 18-24 months total. Thus closer port (Barus) takes longer than distant India (9-12 months). Chinese silk traders needing Dryobalanops aromatica from arrival solved this via monsoon-free land corridor: Barus -> Pasaman West Coast -> Ujung Gading -> Muaro Kiawai -> Nagari Pasaman -> Talu -> Puncak Tonang -> Banio Tinggi (Choke Point Danau Mangguang paleolake 525 masl) -> Patamuan -> Upper Kampar -> Kampar/Siak estuary (15-20 days).